LMFDB - Embedded newform 264.2.z.b.19.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [264,2,Mod(19,264)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(264, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 5, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("264.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 264 = 2^{3} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	264.z (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.10805061336$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			19.9
Character	$\chi$	$=$	264.19
Dual form			264.2.z.b.139.9

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.03357 - 0.965267i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.136519 - 1.99534i) q^{4} +(0.409298 - 0.563350i) q^{5} +(-1.23741 - 0.684696i) q^{6} +(0.510340 - 1.57067i) q^{7} +(-1.78493 - 2.19409i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.120747 - 0.977341i) q^{10} +(2.08351 + 2.58050i) q^{11} +(-1.93986 + 0.486755i) q^{12} +(-4.92015 + 3.57470i) q^{13} +(-0.988641 - 2.11600i) q^{14} +(-0.662258 - 0.215181i) q^{15} +(-3.96273 - 0.544803i) q^{16} +(2.23176 - 3.07176i) q^{17} +(-0.268803 + 1.38843i) q^{18} +(5.66454 - 1.84052i) q^{19} +(-1.06820 - 0.893594i) q^{20} -1.65150 q^{21} +(4.64432 + 0.655979i) q^{22} -8.64584i q^{23} +(-1.53513 + 2.37558i) q^{24} +(1.39525 + 4.29413i) q^{25} +(-1.63476 + 8.44395i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-3.06433 - 1.23273i) q^{28} +(-1.33248 + 4.10095i) q^{29} +(-0.892194 + 0.416852i) q^{30} +(4.09860 + 5.64124i) q^{31} +(-4.62162 + 3.26200i) q^{32} +(1.81036 - 2.77895i) q^{33} +(-0.658392 - 5.32912i) q^{34} +(-0.675953 - 0.930370i) q^{35} +(1.06238 + 1.69450i) q^{36} +(-2.02338 - 0.657436i) q^{37} +(4.07809 - 7.37010i) q^{38} +(4.92015 + 3.57470i) q^{39} +(-1.96661 + 0.107505i) q^{40} +(0.736879 - 0.239427i) q^{41} +(-1.70693 + 1.59413i) q^{42} +10.1720i q^{43} +(5.43341 - 3.80501i) q^{44} +0.696339i q^{45} +(-8.34554 - 8.93605i) q^{46} +(5.29780 - 1.72136i) q^{47} +(0.706411 + 3.93713i) q^{48} +(3.45658 + 2.51135i) q^{49} +(5.58706 + 3.09148i) q^{50} +(-3.61107 - 1.17331i) q^{51} +(6.46103 + 10.3054i) q^{52} +(2.57874 + 3.54933i) q^{53} +(1.40354 - 0.173402i) q^{54} +(2.30650 - 0.117551i) q^{55} +(-4.35710 + 1.68380i) q^{56} +(-3.50088 - 4.81855i) q^{57} +(2.58130 + 5.52480i) q^{58} +(3.78102 - 11.6368i) q^{59} +(-0.519768 + 1.29205i) q^{60} +(-0.239653 - 0.174118i) q^{61} +(9.68148 + 1.87435i) q^{62} +(0.510340 + 1.57067i) q^{63} +(-1.62805 + 7.83259i) q^{64} +4.23488i q^{65} +(-0.811300 - 4.61972i) q^{66} -10.7130 q^{67} +(-5.82451 - 4.87247i) q^{68} +(-8.22268 + 2.67171i) q^{69} +(-1.59670 - 0.309124i) q^{70} +(-1.14044 + 1.56968i) q^{71} +(2.73369 + 0.725900i) q^{72} +(-6.90989 - 2.24516i) q^{73} +(-2.72590 + 1.27360i) q^{74} +(3.65280 - 2.65392i) q^{75} +(-2.89914 - 11.5539i) q^{76} +(5.11640 - 1.95556i) q^{77} +(8.53584 - 1.05457i) q^{78} +(2.76926 - 2.01198i) q^{79} +(-1.92885 + 2.00941i) q^{80} +(0.309017 - 0.951057i) q^{81} +(0.530503 - 0.958748i) q^{82} +(-1.90883 + 2.62729i) q^{83} +(-0.225461 + 3.29529i) q^{84} +(-0.817020 - 2.51453i) q^{85} +(9.81874 + 10.5135i) q^{86} +4.31199 q^{87} +(1.94294 - 9.17742i) q^{88} -6.63247 q^{89} +(0.672153 + 0.719713i) q^{90} +(3.10371 + 9.55222i) q^{91} +(-17.2513 - 1.18032i) q^{92} +(4.09860 - 5.64124i) q^{93} +(3.81406 - 6.89293i) q^{94} +(1.28163 - 3.94444i) q^{95} +(4.53050 + 3.38741i) q^{96} +(-3.48568 + 2.53250i) q^{97} +(5.99672 - 0.740872i) q^{98} +(-3.20237 - 0.863015i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{3} + 4 q^{4} - 12 q^{9} + 4 q^{11} + 6 q^{12} - 16 q^{14} + 20 q^{16} - 5 q^{18} + 25 q^{20} + 3 q^{22} + 20 q^{24} - 4 q^{25} + 4 q^{26} + 12 q^{27} - 25 q^{28} - 10 q^{30} - 4 q^{33} + 4 q^{36}+ \cdots - 16 q^{99}+O(q^{100}) $ 48 * q + 12 * q^3 + 4 * q^4 - 12 * q^9 + 4 * q^11 + 6 * q^12 - 16 * q^14 + 20 * q^16 - 5 * q^18 + 25 * q^20 + 3 * q^22 + 20 * q^24 - 4 * q^25 + 4 * q^26 + 12 * q^27 - 25 * q^28 - 10 * q^30 - 4 * q^33 + 4 * q^36 + 26 * q^38 - 65 * q^40 - 60 * q^41 - 4 * q^42 - 43 * q^44 - 5 * q^46 + 5 * q^48 - 12 * q^49 - 80 * q^50 - 15 * q^52 - 14 * q^56 + 73 * q^58 - 8 * q^59 - 25 * q^60 - 45 * q^62 - 38 * q^64 - 13 * q^66 + 8 * q^67 - 55 * q^68 - 40 * q^70 + 20 * q^72 + 60 * q^74 - 36 * q^75 + 46 * q^78 - 12 * q^81 - 35 * q^82 - 100 * q^83 + 45 * q^84 + 81 * q^86 - 18 * q^88 + 96 * q^89 + 10 * q^90 - 20 * q^91 + 59 * q^92 + 35 * q^94 - 40 * q^97 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/264\mathbb{Z}\right)^\times$.

$n$	$89$	$133$	$145$	$199$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{10}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.03357	−	0.965267i	0.730842	−	0.682547i
$2$	1.03357	−	0.965267i	0.730842	−	0.682547i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	0.136519	−	1.99534i	0.0682596	−	0.997668i
$5$	0.409298	−	0.563350i	0.183044	−	0.251938i	−0.707628	−	0.706585i	$-0.750235\pi$
$5$	0.409298	−	0.563350i	0.183044	−	0.251938i	0.890672	+	0.454647i	$0.150235\pi$
$6$	−1.23741	−	0.684696i	−0.505172	−	0.279526i
$7$	0.510340	−	1.57067i	0.192890	−	0.593656i	−0.807104	−	0.590409i	$-0.798967\pi$
$7$	0.510340	−	1.57067i	0.192890	−	0.593656i	0.999995	−	0.00324682i	$-0.00103350\pi$
$8$	−1.78493	−	2.19409i	−0.631068	−	0.775728i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−0.120747	−	0.977341i	−0.0381835	−	0.309062i
$11$	2.08351	+	2.58050i	0.628201	+	0.778051i
$11$	2.08351	+	2.58050i	0.628201	+	0.778051i
$12$	−1.93986	+	0.486755i	−0.559990	+	0.140514i
$13$	−4.92015	+	3.57470i	−1.36460	+	0.991443i	−0.366468	+	0.930431i	$0.619433\pi$
$13$	−4.92015	+	3.57470i	−1.36460	+	0.991443i	−0.998137	+	0.0610124i	$0.980567\pi$
$14$	−0.988641	−	2.11600i	−0.264225	−	0.565525i
$15$	−0.662258	−	0.215181i	−0.170994	−	0.0555594i
$16$	−3.96273	−	0.544803i	−0.990681	−	0.136201i
$17$	2.23176	−	3.07176i	0.541282	−	0.745011i	−0.447515	−	0.894277i	$-0.647691\pi$
$17$	2.23176	−	3.07176i	0.541282	−	0.745011i	0.988797	+	0.149265i	$0.0476908\pi$
$18$	−0.268803	+	1.38843i	−0.0633575	+	0.327257i
$19$	5.66454	−	1.84052i	1.29954	−	0.422245i	0.424116	−	0.905608i	$-0.360585\pi$
$19$	5.66454	−	1.84052i	1.29954	−	0.422245i	0.875420	+	0.483364i	$0.160585\pi$
$20$	−1.06820	−	0.893594i	−0.238856	−	0.199814i
$21$	−1.65150			−0.360386
$22$	4.64432	+	0.655979i	0.990172	+	0.139855i
$23$		−	8.64584i		−	1.80278i	−0.433006	−	0.901391i	$-0.642547\pi$
$23$		−	8.64584i		−	1.80278i	0.433006	−	0.901391i	$-0.357453\pi$
$24$	−1.53513	+	2.37558i	−0.313357	+	0.484913i
$25$	1.39525	+	4.29413i	0.279049	+	0.858825i
$26$	−1.63476	+	8.44395i	−0.320604	+	1.65599i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−3.06433	−	1.23273i	−0.579104	−	0.232963i
$29$	−1.33248	+	4.10095i	−0.247435	+	0.761526i	0.747791	+	0.663934i	$0.231114\pi$
$29$	−1.33248	+	4.10095i	−0.247435	+	0.761526i	−0.995226	+	0.0975928i	$0.968886\pi$
$30$	−0.892194	+	0.416852i	−0.162892	+	0.0761064i
$31$	4.09860	+	5.64124i	0.736131	+	1.01320i	0.998832	+	0.0483198i	$0.0153867\pi$
$31$	4.09860	+	5.64124i	0.736131	+	1.01320i	−0.262701	+	0.964877i	$0.584613\pi$
$32$	−4.62162	+	3.26200i	−0.816995	+	0.576645i
$33$	1.81036	−	2.77895i	0.315144	−	0.483754i
$34$	−0.658392	−	5.32912i	−0.112913	−	0.913936i
$35$	−0.675953	−	0.930370i	−0.114257	−	0.157261i
$36$	1.06238	+	1.69450i	0.177064	+	0.282417i
$37$	−2.02338	−	0.657436i	−0.332642	−	0.108082i	0.137934	−	0.990441i	$-0.455954\pi$
$37$	−2.02338	−	0.657436i	−0.332642	−	0.108082i	−0.470576	+	0.882360i	$0.655954\pi$
$38$	4.07809	−	7.37010i	0.661553	−	1.19559i
$39$	4.92015	+	3.57470i	0.787855	+	0.572410i
$40$	−1.96661	+	0.107505i	−0.310948	+	0.0169980i
$41$	0.736879	−	0.239427i	0.115081	−	0.0373921i	−0.250910	−	0.968010i	$-0.580730\pi$
$41$	0.736879	−	0.239427i	0.115081	−	0.0373921i	0.365991	+	0.930618i	$0.380730\pi$
$42$	−1.70693	+	1.59413i	−0.263385	+	0.245980i
$43$			10.1720i			1.55122i	0.631211	+	0.775611i	$0.282558\pi$
$43$			10.1720i			1.55122i	−0.631211	+	0.775611i	$0.717442\pi$
$44$	5.43341	−	3.80501i	0.819117	−	0.573627i
$45$			0.696339i			0.103804i
$46$	−8.34554	−	8.93605i	−1.23048	−	1.31755i
$47$	5.29780	−	1.72136i	0.772764	−	0.251086i	0.104016	−	0.994576i	$-0.466831\pi$
$47$	5.29780	−	1.72136i	0.772764	−	0.251086i	0.668748	+	0.743489i	$0.266831\pi$
$48$	0.706411	+	3.93713i	0.101962	+	0.568276i
$49$	3.45658	+	2.51135i	0.493797	+	0.358764i
$50$	5.58706	+	3.09148i	0.790129	+	0.437201i
$51$	−3.61107	−	1.17331i	−0.505651	−	0.164296i
$52$	6.46103	+	10.3054i	0.895983	+	1.42910i
$53$	2.57874	+	3.54933i	0.354217	+	0.487538i	0.948526	−	0.316699i	$-0.102574\pi$
$53$	2.57874	+	3.54933i	0.354217	+	0.487538i	−0.594309	+	0.804237i	$0.702574\pi$
$54$	1.40354	−	0.173402i	0.190998	−	0.0235971i
$55$	2.30650	−	0.117551i	0.311009	−	0.0158505i
$56$	−4.35710	+	1.68380i	−0.582242	+	0.225007i
$57$	−3.50088	−	4.81855i	−0.463703	−	0.638232i
$58$	2.58130	+	5.52480i	0.338942	+	0.725441i
$59$	3.78102	−	11.6368i	0.492247	−	1.51498i	−0.328958	−	0.944345i	$-0.606697\pi$
$59$	3.78102	−	11.6368i	0.492247	−	1.51498i	0.821204	−	0.570634i	$-0.193303\pi$
$60$	−0.519768	+	1.29205i	−0.0671018	+	0.166803i
$61$	−0.239653	−	0.174118i	−0.0306845	−	0.0222936i	0.572337	−	0.820018i	$-0.306037\pi$
$61$	−0.239653	−	0.174118i	−0.0306845	−	0.0222936i	−0.603022	+	0.797725i	$0.706037\pi$
$62$	9.68148	+	1.87435i	1.22955	+	0.238043i
$63$	0.510340	+	1.57067i	0.0642968	+	0.197885i
$64$	−1.62805	+	7.83259i	−0.203507	+	0.979074i
$65$			4.23488i			0.525273i
$66$	−0.811300	−	4.61972i	−0.0998641	−	0.568648i
$67$	−10.7130			−1.30880			−0.654402	−	0.756147i	$-0.727079\pi$
$67$	−10.7130			−1.30880			−0.654402	+	0.756147i	$0.727079\pi$
$68$	−5.82451	−	4.87247i	−0.706326	−	0.590874i
$69$	−8.22268	+	2.67171i	−0.989894	+	0.321636i
$70$	−1.59670	−	0.309124i	−0.190842	−	0.0369473i
$71$	−1.14044	+	1.56968i	−0.135345	+	0.186287i	−0.871310	−	0.490733i	$-0.836729\pi$
$71$	−1.14044	+	1.56968i	−0.135345	+	0.186287i	0.735964	+	0.677020i	$0.236729\pi$
$72$	2.73369	+	0.725900i	0.322169	+	0.0855481i
$73$	−6.90989	−	2.24516i	−0.808741	−	0.262776i	−0.124677	−	0.992197i	$-0.539789\pi$
$73$	−6.90989	−	2.24516i	−0.808741	−	0.262776i	−0.684064	+	0.729422i	$0.739789\pi$
$74$	−2.72590	+	1.27360i	−0.316879	+	0.148053i
$75$	3.65280	−	2.65392i	0.421789	−	0.306448i
$76$	−2.89914	−	11.5539i	−0.332554	−	1.32533i
$77$	5.11640	−	1.95556i	0.583068	−	0.222857i
$78$	8.53584	−	1.05457i	0.966494	−	0.119407i
$79$	2.76926	−	2.01198i	0.311566	−	0.226366i	−0.421002	−	0.907060i	$-0.638322\pi$
$79$	2.76926	−	2.01198i	0.311566	−	0.226366i	0.732568	+	0.680694i	$0.238322\pi$
$80$	−1.92885	+	2.00941i	−0.215652	+	0.224659i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	0.530503	−	0.958748i	0.0585843	−	0.105876i
$83$	−1.90883	+	2.62729i	−0.209522	+	0.288382i	−0.900825	−	0.434183i	$-0.857037\pi$
$83$	−1.90883	+	2.62729i	−0.209522	+	0.288382i	0.691303	+	0.722565i	$0.257037\pi$
$84$	−0.225461	+	3.29529i	−0.0245998	+	0.359545i
$85$	−0.817020	−	2.51453i	−0.0886183	−	0.272739i
$86$	9.81874	+	10.5135i	1.05878	+	1.13370i
$87$	4.31199			0.462294
$88$	1.94294	−	9.17742i	0.207118	−	0.978316i
$89$	−6.63247			−0.703040			−0.351520	−	0.936180i	$-0.614335\pi$
$89$	−6.63247			−0.703040			−0.351520	+	0.936180i	$0.614335\pi$
$90$	0.672153	+	0.719713i	0.0708512	+	0.0758644i
$91$	3.10371	+	9.55222i	0.325357	+	1.00135i
$92$	−17.2513	−	1.18032i	−1.79858	−	0.123057i
$93$	4.09860	−	5.64124i	0.425005	−	0.584970i
$94$	3.81406	−	6.89293i	0.393390	−	0.710952i
$95$	1.28163	−	3.94444i	0.131492	−	0.404691i
$96$	4.53050	+	3.38741i	0.462393	+	0.345726i
$97$	−3.48568	+	2.53250i	−0.353917	+	0.257136i	−0.750511	−	0.660858i	$-0.770192\pi$
$97$	−3.48568	+	2.53250i	−0.353917	+	0.257136i	0.396593	+	0.917994i	$0.370192\pi$
$98$	5.99672	−	0.740872i	0.605761	−	0.0748394i
$99$	−3.20237	−	0.863015i	−0.321851	−	0.0867363i
$100$	8.75870	−	2.19775i	0.875870	−	0.219775i
$101$	−4.21872	+	3.06508i	−0.419778	+	0.304987i	−0.777549	−	0.628823i	$-0.783537\pi$
$101$	−4.21872	+	3.06508i	−0.419778	+	0.304987i	0.357770	+	0.933810i	$0.383537\pi$
$102$	−4.86484	+	2.27296i	−0.481691	+	0.225056i
$103$	−3.29822	−	1.07166i	−0.324983	−	0.105593i	0.141982	−	0.989869i	$-0.454653\pi$
$103$	−3.29822	−	1.07166i	−0.324983	−	0.105593i	−0.466965	+	0.884276i	$0.654653\pi$
$104$	16.6253	+	4.41466i	1.63025	+	0.432893i
$105$	−0.675953	+	0.930370i	−0.0659663	+	0.0907948i
$106$	6.09135	+	1.17930i	0.591645	+	0.114543i
$107$	−7.88188	+	2.56098i	−0.761970	+	0.247579i	−0.664124	−	0.747623i	$-0.731195\pi$
$107$	−7.88188	+	2.56098i	−0.761970	+	0.247579i	−0.0978460	+	0.995202i	$0.531195\pi$
$108$	1.28327	−	1.53402i	0.123483	−	0.147611i
$109$	−17.7781			−1.70284			−0.851419	−	0.524487i	$-0.824257\pi$
$109$	−17.7781			−1.70284			−0.851419	+	0.524487i	$0.824257\pi$
$110$	2.27046	−	2.34789i	0.216479	−	0.223862i
$111$			2.12751i			0.201934i
$112$	−2.87804	+	5.94608i	−0.271949	+	0.561852i
$113$	−2.30521	−	7.09472i	−0.216856	−	0.667415i	−0.999017	−	0.0443379i	$-0.985882\pi$
$113$	−2.30521	−	7.09472i	−0.216856	−	0.667415i	0.782160	−	0.623077i	$-0.214118\pi$
$114$	−8.26958	−	1.60101i	−0.774517	−	0.149948i
$115$	−4.87063	−	3.53872i	−0.454189	−	0.329988i
$116$	8.00085	+	3.21860i	0.742860	+	0.298839i
$117$	1.87933	−	5.78399i	0.173744	−	0.534730i
$118$	−7.32466	−	15.6771i	−0.674290	−	1.44319i
$119$	−3.68575	−	5.07300i	−0.337872	−	0.465041i
$120$	0.709958	+	1.83713i	0.0648100	+	0.167707i
$121$	−2.31799	+	10.7530i	−0.210726	+	0.977545i
$122$	−0.415768	+	0.0513666i	−0.0376419	+	0.00465051i
$123$	−0.455416	−	0.626827i	−0.0410635	−	0.0565191i
$124$	11.8157	−	7.40795i	1.06108	−	0.665253i
$125$	6.30146	+	2.04747i	0.563619	+	0.183131i
$126$	2.04358	+	1.13077i	0.182057	+	0.100737i
$127$	−5.14844	−	3.74056i	−0.456850	−	0.331921i	0.335444	−	0.942060i	$-0.391114\pi$
$127$	−5.14844	−	3.74056i	−0.456850	−	0.331921i	−0.792294	+	0.610139i	$0.791114\pi$
$128$	5.87784	+	9.66701i	0.519533	+	0.854451i
$129$	9.67419	−	3.14334i	0.851765	−	0.276755i
$130$	4.08779	+	4.37703i	0.358523	+	0.383891i
$131$			0.239732i			0.0209455i	0.999945	+	0.0104727i	$0.00333363\pi$
$131$			0.239732i			0.0209455i	−0.999945	+	0.0104727i	$0.996666\pi$
$132$	−5.29779	−	3.99166i	−0.461114	−	0.347430i
$133$		−	9.83639i		−	0.852923i
$134$	−11.0726	+	10.3409i	−0.956528	+	0.893320i
$135$	0.662258	−	0.215181i	0.0569981	−	0.0185198i
$136$	−10.7233	+	0.586186i	−0.919512	+	0.0502651i
$137$	−2.39415	−	1.73945i	−0.204546	−	0.148611i	0.480797	−	0.876832i	$-0.340348\pi$
$137$	−2.39415	−	1.73945i	−0.204546	−	0.148611i	−0.685343	+	0.728221i	$0.740348\pi$
$138$	−5.91977	+	10.6985i	−0.503925	+	0.910715i
$139$	1.50194	+	0.488010i	0.127393	+	0.0413925i	0.372020	−	0.928225i	$-0.378665\pi$
$139$	1.50194	+	0.488010i	0.127393	+	0.0413925i	−0.244627	+	0.969617i	$0.578665\pi$
$140$	−1.94868	+	1.22174i	−0.164694	+	0.103256i
$141$	−3.27422	−	4.50658i	−0.275739	−	0.379522i
$142$	0.336441	+	2.72320i	0.0282335	+	0.228526i
$143$	−19.4757	−	5.24855i	−1.62864	−	0.438906i
$144$	3.52614	−	1.88848i	0.293845	−	0.157373i
$145$	1.76489	+	2.42916i	0.146566	+	0.201731i
$146$	−9.30900	+	4.34936i	−0.770419	+	0.359956i
$147$	1.32029	−	4.06345i	0.108896	−	0.335148i
$148$	−1.58804	+	3.94757i	−0.130536	+	0.324488i
$149$	14.7822	+	10.7399i	1.21101	+	0.879849i	0.995322	−	0.0966133i	$-0.0308010\pi$
$149$	14.7822	+	10.7399i	1.21101	+	0.879849i	0.215687	+	0.976463i	$0.430801\pi$
$150$	1.21368	−	6.26893i	0.0990962	−	0.511856i
$151$	4.68718	+	14.4256i	0.381437	+	1.17394i	0.939032	+	0.343829i	$0.111724\pi$
$151$	4.68718	+	14.4256i	0.381437	+	1.17394i	−0.557595	+	0.830113i	$0.688276\pi$
$152$	−14.1491	−	9.14331i	−1.14764	−	0.741620i
$153$			3.79690i			0.306962i
$154$	3.40051	−	6.95990i	0.274021	−	0.560845i
$155$	4.85554			0.390007
$156$	7.80442	−	9.32934i	0.624854	−	0.746945i
$157$	6.33215	−	2.05744i	0.505360	−	0.164202i	−0.0452308	−	0.998977i	$-0.514402\pi$
$157$	6.33215	−	2.05744i	0.505360	−	0.164202i	0.550591	+	0.834775i	$0.314402\pi$
$158$	0.920110	−	4.75259i	0.0732000	−	0.378096i
$159$	2.57874	−	3.54933i	0.204507	−	0.281480i
$160$	−0.0539720	+	3.93872i	−0.00426686	+	0.311383i
$161$	−13.5797	−	4.41232i	−1.07023	−	0.347739i
$162$	−0.598634	−	1.28126i	−0.0470331	−	0.100666i
$163$	−0.612537	+	0.445034i	−0.0479776	+	0.0348578i	−0.611516	−	0.791232i	$-0.709440\pi$
$163$	−0.612537	+	0.445034i	−0.0479776	+	0.0348578i	0.563538	+	0.826090i	$0.309440\pi$
$164$	−0.377138	−	1.50301i	−0.0294495	−	0.117365i
$165$	−0.824545	−	2.15729i	−0.0641908	−	0.167945i
$166$	0.563125	+	4.55801i	0.0437069	+	0.353770i
$167$	−11.1349	+	8.08998i	−0.861644	+	0.626021i	−0.928332	−	0.371753i	$-0.878757\pi$
$167$	−11.1349	+	8.08998i	−0.861644	+	0.626021i	0.0666874	+	0.997774i	$0.478757\pi$
$168$	2.94780	+	3.62353i	0.227428	+	0.279561i
$169$	7.41220	−	22.8124i	0.570169	−	1.75480i
$170$	−3.27164	−	1.81029i	−0.250923	−	0.138843i
$171$	−3.50088	+	4.81855i	−0.267719	+	0.368484i
$172$	20.2966	+	1.38868i	1.54760	+	0.105886i
$173$	1.35890	+	4.18227i	0.103315	+	0.317972i	0.989331	−	0.145683i	$-0.0465379\pi$
$173$	1.35890	+	4.18227i	0.103315	+	0.317972i	−0.886016	+	0.463655i	$0.846538\pi$
$174$	4.45673	−	4.16222i	0.337864	−	0.315537i
$175$	7.45669			0.563672
$176$	−6.85051	−	11.3609i	−0.516376	−	0.856362i
$177$	−12.2356			−0.919686
$178$	−6.85509	+	6.40210i	−0.513811	+	0.479858i
$179$	−5.23266	−	16.1045i	−0.391107	−	1.20370i	−0.931952	−	0.362582i	$-0.881895\pi$
$179$	−5.23266	−	16.1045i	−0.391107	−	1.20370i	0.540845	−	0.841122i	$-0.318105\pi$
$180$	1.38943	+	0.0950636i	0.103562	+	0.00708562i
$181$	10.7847	−	14.8439i	0.801620	−	1.10334i	−0.190943	−	0.981601i	$-0.561155\pi$
$181$	10.7847	−	14.8439i	0.801620	−	1.10334i	0.992563	−	0.121734i	$-0.0388455\pi$
$182$	12.4283	+	6.87695i	0.921249	+	0.509754i
$183$	−0.0915394	+	0.281729i	−0.00676679	+	0.0208260i
$184$	−18.9697	+	15.4322i	−1.39847	+	1.13768i
$185$	−1.19853	+	0.870785i	−0.0881178	+	0.0640214i
$186$	−1.20913	−	9.78684i	−0.0886575	−	0.717606i
$187$	12.5766	−	0.640964i	0.919691	−	0.0468719i
$188$	−2.71144	−	10.8059i	−0.197752	−	0.788100i
$189$	1.33609	−	0.970725i	0.0971861	−	0.0706098i
$190$	−2.48279	−	5.31396i	−0.180121	−	0.385515i
$191$	−23.5927	−	7.66573i	−1.70711	−	0.554673i	−0.717259	−	0.696806i	$-0.754604\pi$
$191$	−23.5927	−	7.66573i	−1.70711	−	0.554673i	−0.989847	+	0.142134i	$0.954604\pi$
$192$	7.95233	−	0.872033i	0.573910	−	0.0629336i
$193$	0.0138035	−	0.0189988i	0.000993595	−	0.00136757i	−0.808520	−	0.588469i	$-0.799731\pi$
$193$	0.0138035	−	0.0189988i	0.000993595	−	0.00136757i	0.809514	+	0.587101i	$0.199731\pi$
$194$	−1.15815	+	5.98212i	−0.0831503	+	0.429491i
$195$	4.02761	−	1.30865i	0.288423	−	0.0937145i
$196$	5.48287	−	6.55418i	0.391634	−	0.468156i
$197$	−0.183455			−0.0130706			−0.00653530	−	0.999979i	$-0.502080\pi$
$197$	−0.183455			−0.0130706			−0.00653530	+	0.999979i	$0.502080\pi$
$198$	−4.14291	+	2.19916i	−0.294424	+	0.156288i
$199$		−	14.8031i		−	1.04936i	−0.851298	−	0.524682i	$-0.824184\pi$
$199$		−	14.8031i		−	1.04936i	0.851298	−	0.524682i	$-0.175816\pi$
$200$	6.93128	−	10.7260i	0.490115	−	0.758443i
$201$	3.31050	+	10.1887i	0.233505	+	0.718655i
$202$	−1.40171	+	7.24015i	−0.0986237	+	0.509415i
$203$	5.76120	+	4.18575i	0.404357	+	0.293782i
$204$	−2.83412	+	7.04512i	−0.198428	+	0.493257i
$205$	0.166722	−	0.513118i	0.0116444	−	0.0358377i
$206$	−4.44336	+	2.07603i	−0.309583	+	0.144644i
$207$	5.08190	+	6.99463i	0.353216	+	0.486160i
$208$	21.4447	−	11.4850i	1.48692	−	0.796344i
$209$	16.5516	+	10.7826i	1.14490	+	0.745850i
$210$	0.199413	+	1.61407i	0.0137608	+	0.111382i
$211$	−6.77305	−	9.32230i	−0.466276	−	0.641774i	0.509519	−	0.860459i	$-0.329823\pi$
$211$	−6.77305	−	9.32230i	−0.466276	−	0.641774i	−0.975795	+	0.218685i	$0.929823\pi$
$212$	7.43415	−	4.66090i	0.510580	−	0.320112i
$213$	1.84527	+	0.599565i	0.126436	+	0.0410815i
$214$	−5.67442	+	10.2551i	−0.387895	+	0.701021i
$215$	5.73042	+	4.16340i	0.390812	+	0.283941i
$216$	−0.154385	−	2.82421i	−0.0105046	−	0.192163i
$217$	10.9522	−	3.55858i	0.743483	−	0.241572i
$218$	−18.3749	+	17.1607i	−1.24450	+	1.16227i
$219$			7.26548i			0.490956i
$220$	0.0803288	−	4.61829i	0.00541577	−	0.311365i
$221$			23.0914i			1.55330i
$222$	2.05361	+	2.19892i	0.137830	+	0.147582i
$223$	9.63345	−	3.13010i	0.645104	−	0.209607i	0.0318497	−	0.999493i	$-0.489860\pi$
$223$	9.63345	−	3.13010i	0.645104	−	0.209607i	0.613254	+	0.789886i	$0.289860\pi$
$224$	2.76491	+	8.92375i	0.184738	+	0.596243i
$225$	−3.65280	−	2.65392i	−0.243520	−	0.176928i
$226$	−9.23089	−	5.10772i	−0.614030	−	0.339760i
$227$	−8.77003	−	2.84955i	−0.582087	−	0.189132i	0.00314828	−	0.999995i	$-0.498998\pi$
$227$	−8.77003	−	2.84955i	−0.582087	−	0.189132i	−0.585235	+	0.810863i	$0.698998\pi$
$228$	−10.0926	+	6.32761i	−0.668396	+	0.419056i
$229$	15.0976	+	20.7800i	0.997676	+	1.37318i	0.926740	+	0.375703i	$0.122599\pi$
$229$	15.0976	+	20.7800i	0.997676	+	1.37318i	0.0709359	+	0.997481i	$0.477401\pi$
$230$	−8.44994	+	1.04396i	−0.557172	+	0.0688365i
$231$	−3.44090	−	4.26169i	−0.226395	−	0.280398i
$232$	11.3762	−	4.39632i	0.746885	−	0.288633i
$233$	14.1060	+	19.4152i	0.924112	+	1.27193i	0.962112	+	0.272654i	$0.0879013\pi$
$233$	14.1060	+	19.4152i	0.924112	+	1.27193i	−0.0380001	+	0.999278i	$0.512099\pi$
$234$	−3.64068	−	7.79219i	−0.237999	−	0.509391i
$235$	1.19865	−	3.68907i	0.0781913	−	0.240648i
$236$	−22.7031	−	9.13304i	−1.47785	−	0.594510i
$237$	−2.76926	−	2.01198i	−0.179882	−	0.130692i
$238$	−8.70626	−	1.68555i	−0.564343	−	0.109258i
$239$	4.93373	+	15.1845i	0.319137	+	0.982201i	0.974018	+	0.226470i	$0.0727185\pi$
$239$	4.93373	+	15.1845i	0.319137	+	0.982201i	−0.654882	+	0.755731i	$0.727282\pi$
$240$	2.50711	+	1.21350i	0.161834	+	0.0783312i
$241$			9.42736i			0.607269i	0.952789	+	0.303635i	$0.0982003\pi$
$241$			9.42736i			0.607269i	−0.952789	+	0.303635i	$0.901800\pi$
$242$	7.98372	+	13.3514i	0.513213	+	0.858261i
$243$	−1.00000			−0.0641500
$244$	−0.380142	+	0.454418i	−0.0243361	+	0.0290911i
$245$	2.82954	−	0.919373i	0.180773	−	0.0587366i
$246$	−1.07576	−	0.208269i	−0.0685878	−	0.0132787i
$247$	−21.2911	+	29.3047i	−1.35472	+	1.86461i
$248$	5.06167	−	19.0619i	0.321416	−	1.21043i
$249$	3.08856	+	1.00353i	0.195729	+	0.0635964i
$250$	8.48933	−	3.96639i	0.536912	−	0.250857i
$251$	−3.20392	+	2.32778i	−0.202229	+	0.146928i	−0.684291	−	0.729209i	$-0.739888\pi$
$251$	−3.20392	+	2.32778i	−0.202229	+	0.146928i	0.482062	+	0.876137i	$0.339888\pi$
$252$	3.20368	−	0.803874i	0.201813	−	0.0506393i
$253$	22.3106	−	18.0137i	1.40266	−	1.13251i
$254$	−8.93190	+	1.10350i	−0.560437	+	0.0692399i
$255$	−2.13899	+	1.55406i	−0.133949	+	0.0973193i
$256$	15.4064	+	4.31781i	0.962899	+	0.269863i
$257$	6.26844	−	19.2923i	0.391015	−	1.20342i	−0.541008	−	0.841018i	$-0.681957\pi$
$257$	6.26844	−	19.2923i	0.391015	−	1.20342i	0.932022	−	0.362401i	$-0.118043\pi$
$258$	6.96476	−	12.5870i	0.433607	−	0.783634i
$259$	−2.06522	+	2.84254i	−0.128327	+	0.176627i
$260$	8.45001	+	0.578143i	0.524048	+	0.0358549i
$261$	−1.33248	−	4.10095i	−0.0824783	−	0.253842i
$262$	0.231405	+	0.247779i	0.0142963	+	0.0153078i
$263$	4.86501			0.299989			0.149995	−	0.988687i	$-0.452074\pi$
$263$	4.86501			0.299989			0.149995	+	0.988687i	$0.452074\pi$
$264$	−9.32864	+	0.988136i	−0.574138	+	0.0608156i
$265$	3.05499			0.187667
$266$	−9.49475	−	10.1666i	−0.582160	−	0.623352i
$267$	2.04954	+	6.30785i	0.125430	+	0.386034i
$268$	−1.46253	+	21.3761i	−0.0893384	+	1.30575i
$269$	16.9712	−	23.3589i	1.03475	−	1.42422i	0.133435	−	0.991058i	$-0.457399\pi$
$269$	16.9712	−	23.3589i	1.03475	−	1.42422i	0.901318	−	0.433158i	$-0.142601\pi$
$270$	0.476781	−	0.861659i	0.0290159	−	0.0524389i
$271$	−4.51837	+	13.9061i	−0.274472	+	0.844737i	0.714887	+	0.699240i	$0.246478\pi$
$271$	−4.51837	+	13.9061i	−0.274472	+	0.844737i	−0.989359	+	0.145497i	$0.953522\pi$
$272$	−10.5174	+	10.9567i	−0.637709	+	0.664346i
$273$	8.12561	−	5.90360i	0.491784	−	0.357302i
$274$	−4.15354	+	0.513155i	−0.250925	+	0.0310008i
$275$	−8.17400	+	12.5473i	−0.492911	+	0.756630i
$276$	4.20841	+	16.7717i	0.253316	+	1.00954i
$277$	−22.3661	+	16.2499i	−1.34385	+	0.976363i	−0.344556	+	0.938766i	$0.611970\pi$
$277$	−22.3661	+	16.2499i	−1.34385	+	0.976363i	−0.999293	+	0.0375974i	$0.988030\pi$
$278$	2.02342	−	0.945383i	0.121356	−	0.0567003i
$279$	−6.63168	−	2.15476i	−0.397028	−	0.129002i
$280$	−0.834785	+	3.14375i	−0.0498880	+	0.187875i
$281$	−16.8765	+	23.2286i	−1.00677	+	1.38570i	−0.0856916	+	0.996322i	$0.527310\pi$
$281$	−16.8765	+	23.2286i	−1.00677	+	1.38570i	−0.921078	+	0.389378i	$0.872690\pi$
$282$	−7.73418	−	1.49735i	−0.460564	−	0.0891659i
$283$	14.9354	−	4.85281i	0.887818	−	0.288469i	0.170618	−	0.985337i	$-0.445424\pi$
$283$	14.9354	−	4.85281i	0.887818	−	0.288469i	0.717200	+	0.696868i	$0.245424\pi$
$284$	2.97635	+	2.48985i	0.176614	+	0.147746i
$285$	−4.14743			−0.245673
$286$	−25.1957	+	13.3745i	−1.48985	+	0.790852i
$287$		−	1.27958i		−	0.0755312i
$288$	1.82161	−	5.35553i	0.107340	−	0.315578i
$289$	0.798350	+	2.45707i	0.0469618	+	0.144533i
$290$	4.16892	+	0.807110i	0.244807	+	0.0473951i
$291$	3.48568	+	2.53250i	0.204334	+	0.148458i
$292$	−5.42317	+	13.4810i	−0.317367	+	0.788918i
$293$	5.97643	−	18.3936i	0.349147	−	1.07456i	−0.610179	−	0.792264i	$-0.708902\pi$
$293$	5.97643	−	18.3936i	0.349147	−	1.07456i	0.959326	−	0.282300i	$-0.0910975\pi$
$294$	−2.55770	−	5.47428i	−0.149168	−	0.319267i
$295$	−5.00802	−	6.89294i	−0.291578	−	0.401323i
$296$	2.16912	+	5.61296i	0.126077	+	0.326246i
$297$	0.168812	+	3.31233i	0.00979548	+	0.192201i
$298$	25.6453	−	3.16838i	1.48559	−	0.183539i
$299$	30.9063	+	42.5388i	1.78736	+	2.46008i
$300$	−4.79678	−	7.65088i	−0.276942	−	0.441723i
$301$	15.9769	+	5.19120i	0.920892	+	0.299216i
$302$	18.7691	+	10.3855i	1.08004	+	0.597618i
$303$	4.21872	+	3.06508i	0.242359	+	0.176084i
$304$	−23.4497	+	4.20742i	−1.34494	+	0.241312i
$305$	−0.196179	+	0.0637424i	−0.0112332	+	0.00364988i
$306$	3.66503	+	3.92435i	0.209516	+	0.224340i
$307$		−	17.8955i		−	1.02135i	−0.859774	−	0.510675i	$-0.829396\pi$
$307$		−	17.8955i		−	1.02135i	0.859774	−	0.510675i	$-0.170604\pi$
$308$	−3.20351	−	10.4759i	−0.182537	−	0.596920i
$309$			3.46795i			0.197285i
$310$	5.01853	−	4.68690i	0.285033	−	0.266198i
$311$	−0.940857	+	0.305703i	−0.0533511	+	0.0173348i	−0.335571	−	0.942015i	$-0.608929\pi$
$311$	−0.940857	+	0.305703i	−0.0533511	+	0.0173348i	0.282220	+	0.959350i	$0.408929\pi$
$312$	−0.938916	−	17.1758i	−0.0531557	−	0.972390i
$313$	−10.9210	−	7.93456i	−0.617291	−	0.448488i	0.234683	−	0.972072i	$-0.424595\pi$
$313$	−10.9210	−	7.93456i	−0.617291	−	0.448488i	−0.851974	+	0.523584i	$0.824595\pi$
$314$	4.55872	−	8.23871i	0.257263	−	0.464938i
$315$	1.09372	+	0.355370i	0.0616239	+	0.0200228i
$316$	−3.63652	−	5.80027i	−0.204570	−	0.326290i
$317$	−5.19658	−	7.15248i	−0.291869	−	0.401724i	0.637751	−	0.770243i	$-0.279865\pi$
$317$	−5.19658	−	7.15248i	−0.291869	−	0.401724i	−0.929620	+	0.368519i	$0.879865\pi$
$318$	−0.760753	−	6.15764i	−0.0426609	−	0.345304i
$319$	−13.3587	+	5.10589i	−0.747945	+	0.285875i
$320$	3.74613	+	4.12302i	0.209415	+	0.230484i
$321$	4.87127	+	6.70473i	0.271888	+	0.374221i
$322$	−18.2946	+	8.54763i	−1.01952	+	0.476341i
$323$	6.98828	−	21.5077i	0.388839	−	1.19672i
$324$	−1.85549	−	0.746430i	−0.103083	−	0.0414683i
$325$	−22.2150	−	16.1402i	−1.23227	−	0.895295i
$326$	−0.203521	+	1.05123i	−0.0112720	+	0.0582225i
$327$	5.49375	+	16.9080i	0.303805	+	0.935016i
$328$	−1.84060	−	1.18942i	−0.101630	−	0.0656747i
$329$		−	9.19955i		−	0.507188i
$330$	−2.93458	−	1.43379i	−0.161543	−	0.0789278i
$331$	9.05146			0.497513			0.248757	−	0.968566i	$-0.419978\pi$
$331$	9.05146			0.497513			0.248757	+	0.968566i	$0.419978\pi$
$332$	4.98172	+	4.16744i	0.273408	+	0.228718i
$333$	2.02338	−	0.657436i	0.110881	−	0.0360273i
$334$	−3.69967	+	19.1097i	−0.202437	+	1.04564i
$335$	−4.38482	+	6.03518i	−0.239568	+	0.329737i
$336$	6.54442	+	0.899739i	0.357027	+	0.0490848i
$337$	−12.9875	−	4.21989i	−0.707474	−	0.229872i	−0.0668898	−	0.997760i	$-0.521308\pi$
$337$	−12.9875	−	4.21989i	−0.707474	−	0.229872i	−0.640584	+	0.767888i	$0.721308\pi$
$338$	−14.3591	−	30.7329i	−0.781030	−	1.67165i
$339$	−6.03513	+	4.38478i	−0.327783	+	0.238149i
$340$	−5.12887	+	1.28695i	−0.278152	+	0.0697945i
$341$	−6.01777	+	22.3300i	−0.325880	+	1.20924i
$342$	1.03279	+	8.35957i	0.0558471	+	0.452034i
$343$	15.0611	−	10.9426i	0.813225	−	0.590842i
$344$	22.3184	−	18.1564i	1.20333	−	0.978927i
$345$	−1.86042	+	5.72577i	−0.100161	+	0.308265i
$346$	5.44152	+	3.01095i	0.292538	+	0.161870i
$347$	1.37075	−	1.88668i	0.0735859	−	0.101282i	−0.770638	−	0.637274i	$-0.780062\pi$
$347$	1.37075	−	1.88668i	0.0735859	−	0.101282i	0.844223	+	0.535991i	$0.180062\pi$
$348$	0.588669	−	8.60386i	0.0315560	−	0.461216i
$349$	−4.49635	−	13.8383i	−0.240684	−	0.740750i	−0.996316	−	0.0857534i	$-0.972670\pi$
$349$	−4.49635	−	13.8383i	−0.240684	−	0.740750i	0.755632	−	0.654996i	$-0.227330\pi$
$350$	7.70698	−	7.19769i	0.411955	−	0.384733i
$351$	−6.08164			−0.324614
$352$	−18.0468	−	5.12970i	−0.961896	−	0.273414i
$353$	23.7432			1.26372			0.631861	−	0.775082i	$-0.282291\pi$
$353$	23.7432			1.26372			0.631861	+	0.775082i	$0.282291\pi$
$354$	−12.6463	+	11.8106i	−0.672145	+	0.627729i
$355$	0.417501	+	1.28494i	0.0221586	+	0.0681973i
$356$	−0.905459	+	13.2340i	−0.0479892	+	0.701400i
$357$	−3.68575	+	5.07300i	−0.195071	+	0.268492i
$358$	−20.9534	−	11.5941i	−1.10742	−	0.612768i
$359$	3.27128	−	10.0680i	0.172652	−	0.531367i	−0.826867	−	0.562398i	$-0.809879\pi$
$359$	3.27128	−	10.0680i	0.172652	−	0.531367i	0.999518	+	0.0310309i	$0.00987904\pi$
$360$	1.52783	−	1.24292i	0.0805237	−	0.0655074i
$361$	13.3282	−	9.68351i	0.701484	−	0.509658i
$362$	−3.18159	−	25.7522i	−0.167221	−	1.35351i
$363$	10.9430	−	1.11832i	0.574359	−	0.0586967i
$364$	19.4836	−	4.88887i	1.02122	−	0.256247i
$365$	−4.09301	+	2.97375i	−0.214238	+	0.155653i
$366$	0.177332	+	0.379546i	0.00926929	+	0.0198392i
$367$	24.8159	+	8.06317i	1.29538	+	0.420894i	0.873971	−	0.485978i	$-0.161536\pi$
$367$	24.8159	+	8.06317i	1.29538	+	0.420894i	0.421407	+	0.906872i	$0.361536\pi$
$368$	−4.71028	+	34.2611i	−0.245540	+	1.78598i
$369$	−0.455416	+	0.626827i	−0.0237080	+	0.0326313i
$370$	−0.398223	+	2.05692i	−0.0207026	+	0.106934i
$371$	6.89085	−	2.23897i	0.357755	−	0.116242i
$372$	−10.6966	−	8.94822i	−0.554595	−	0.463944i
$373$	16.7165			0.865549			0.432774	−	0.901502i	$-0.357535\pi$
$373$	16.7165			0.865549			0.432774	+	0.901502i	$0.357535\pi$
$374$	12.3800	−	12.8022i	0.640156	−	0.661988i
$375$		−	6.62574i		−	0.342152i
$376$	−13.2330	−	8.55134i	−0.682441	−	0.441002i
$377$	−8.10365	−	24.9405i	−0.417359	−	1.28450i
$378$	0.443927	−	2.29299i	0.0228331	−	0.117939i
$379$	−20.2745	−	14.7303i	−1.04143	−	0.756643i	−0.0708660	−	0.997486i	$-0.522576\pi$
$379$	−20.2745	−	14.7303i	−1.04143	−	0.756643i	−0.970564	+	0.240842i	$0.922576\pi$
$380$	−7.69552	−	3.09577i	−0.394772	−	0.158810i
$381$	−1.96653	+	6.05236i	−0.100748	+	0.310072i
$382$	−31.7841	+	14.8502i	−1.62622	+	0.759802i
$383$	−5.14355	−	7.07949i	−0.262823	−	0.361745i	0.657127	−	0.753780i	$-0.271771\pi$
$383$	−5.14355	−	7.07949i	−0.262823	−	0.361745i	−0.919950	+	0.392035i	$0.871771\pi$
$384$	7.37752	−	8.57743i	0.376482	−	0.437715i
$385$	0.992468	−	3.68273i	0.0505808	−	0.187689i
$386$	−0.00407215	−	0.0329606i	−0.000207267	−	0.00167765i
$387$	−5.97898	−	8.22936i	−0.303929	−	0.418322i
$388$	4.57732	+	7.30084i	0.232378	+	0.370644i
$389$	21.4991	+	6.98549i	1.09005	+	0.354179i	0.798265	−	0.602306i	$-0.205751\pi$
$389$	21.4991	+	6.98549i	1.09005	+	0.354179i	0.291784	+	0.956484i	$0.405751\pi$
$390$	2.89961	−	5.24030i	0.146827	−	0.265353i
$391$	−26.5579	−	19.2955i	−1.34309	−	0.975814i
$392$	−0.659621	−	12.0666i	−0.0333159	−	0.609456i
$393$	0.227998	−	0.0740812i	0.0115010	−	0.00373690i
$394$	−0.189613	+	0.177083i	−0.00955254	+	0.00892130i
$395$		−	2.38356i		−	0.119930i
$396$	−2.15919	+	6.27199i	−0.108503	+	0.315180i
$397$		−	2.78536i		−	0.139793i	−0.997554	−	0.0698965i	$-0.977733\pi$
$397$		−	2.78536i		−	0.139793i	0.997554	−	0.0698965i	$-0.0222669\pi$
$398$	−14.2889	−	15.3000i	−0.716240	−	0.766919i
$399$	−9.35497	+	3.03961i	−0.468334	+	0.152171i
$400$	−3.18953	−	17.7766i	−0.159476	−	0.888829i
$401$	5.19019	+	3.77089i	0.259186	+	0.188309i	0.709788	−	0.704415i	$-0.248791\pi$
$401$	5.19019	+	3.77089i	0.259186	+	0.188309i	−0.450602	+	0.892725i	$0.648791\pi$
$402$	13.2564	+	7.33516i	0.661171	+	0.365845i
$403$	−40.3315	−	13.1045i	−2.00905	−	0.652781i
$404$	5.53992	+	8.83620i	0.275621	+	0.439617i
$405$	−0.409298	−	0.563350i	−0.0203382	−	0.0279931i
$406$	9.99495	−	1.23484i	0.496041	−	0.0612840i
$407$	−2.51921	−	6.59111i	−0.124873	−	0.326709i
$408$	3.87117	+	10.0173i	0.191651	+	0.495929i
$409$	−17.5440	−	24.1473i	−0.867496	−	1.19401i	−0.979730	−	0.200324i	$-0.935801\pi$
$409$	−17.5440	−	24.1473i	−0.867496	−	1.19401i	0.112234	−	0.993682i	$-0.464199\pi$
$410$	−0.322977	−	0.691272i	−0.0159507	−	0.0341395i
$411$	−0.914483	+	2.81449i	−0.0451081	+	0.138829i
$412$	−2.58858	+	6.43474i	−0.127530	+	0.317017i
$413$	−16.3479	−	11.8774i	−0.804426	−	0.584450i
$414$	12.0042	+	2.32403i	0.589972	+	0.114220i
$415$	0.698800	+	2.15068i	0.0343027	+	0.105573i
$416$	11.0784	−	32.5704i	0.543164	−	1.59690i
$417$		−	1.57923i		−	0.0773354i
$418$	27.5153	−	4.83215i	1.34582	−	0.236348i
$419$	−2.52141			−0.123179			−0.0615895	−	0.998102i	$-0.519617\pi$
$419$	−2.52141			−0.123179			−0.0615895	+	0.998102i	$0.519617\pi$
$420$	1.76412	+	1.47577i	0.0860802	+	0.0720101i
$421$	−28.8541	+	9.37526i	−1.40626	+	0.456922i	−0.911210	−	0.411942i	$-0.864851\pi$
$421$	−28.8541	+	9.37526i	−1.40626	+	0.456922i	−0.495051	+	0.868864i	$0.664851\pi$
$422$	−15.9989	−	3.09742i	−0.778815	−	0.150780i
$423$	−3.27422	+	4.50658i	−0.159198	+	0.219117i
$424$	3.18468	−	11.9933i	0.154662	−	0.582446i
$425$	16.3044	+	5.29762i	0.790879	+	0.256972i
$426$	2.48595	−	1.16149i	0.120445	−	0.0562744i
$427$	−0.395786	+	0.287555i	−0.0191534	+	0.0139158i
$428$	4.03398	+	16.0766i	0.194990	+	0.777092i
$429$	1.02666	+	20.1444i	0.0495674	+	0.972580i
$430$	9.94156	−	1.22824i	0.479425	−	0.0592311i
$431$	21.0004	−	15.2577i	1.01155	−	0.734937i	0.0470191	−	0.998894i	$-0.485028\pi$
$431$	21.0004	−	15.2577i	1.01155	−	0.734937i	0.964534	+	0.263957i	$0.0850278\pi$
$432$	−2.88568	−	2.76999i	−0.138838	−	0.133271i
$433$	−9.50922	+	29.2664i	−0.456984	+	1.40645i	0.411806	+	0.911271i	$0.364898\pi$
$433$	−9.50922	+	29.2664i	−0.456984	+	1.40645i	−0.868790	+	0.495180i	$0.835102\pi$
$434$	7.88483	−	14.2498i	0.378484	−	0.684013i
$435$	1.76489	−	2.42916i	0.0846199	−	0.116469i
$436$	−2.42706	+	35.4734i	−0.116235	+	1.69887i
$437$	−15.9129	−	48.9747i	−0.761215	−	2.34278i
$438$	7.01313	+	7.50936i	0.335100	+	0.358811i
$439$	13.9098			0.663880			0.331940	−	0.943301i	$-0.392297\pi$
$439$	13.9098			0.663880			0.331940	+	0.943301i	$0.392297\pi$
$440$	−4.37486	−	4.85085i	−0.208563	−	0.231255i
$441$	−4.27256			−0.203455
$442$	22.2894	+	23.8665i	1.06020	+	1.13521i
$443$	2.80215	+	8.62415i	0.133134	+	0.409746i	0.995295	−	0.0968892i	$-0.0308893\pi$
$443$	2.80215	+	8.62415i	0.133134	+	0.409746i	−0.862161	+	0.506635i	$0.830889\pi$
$444$	4.24509	+	0.290446i	0.201463	+	0.0137839i
$445$	−2.71465	+	3.73640i	−0.128687	+	0.177122i
$446$	6.93543	−	12.5340i	0.328402	−	0.593503i
$447$	5.64631	−	17.3776i	0.267062	−	0.821931i
$448$	11.4715	+	6.55441i	0.541978	+	0.309667i
$449$	−14.5319	+	10.5580i	−0.685803	+	0.498265i	−0.875278	−	0.483621i	$-0.839321\pi$
$449$	−14.5319	+	10.5580i	−0.685803	+	0.498265i	0.189475	+	0.981886i	$0.439321\pi$
$450$	−6.33715	+	0.782931i	−0.298736	+	0.0369077i
$451$	2.15313	+	1.40267i	0.101387	+	0.0660492i
$452$	−14.4711	+	3.63111i	−0.680661	+	0.170793i
$453$	12.2712	−	8.91554i	0.576551	−	0.418889i
$454$	−11.8150	+	5.52021i	−0.554505	+	0.259076i
$455$	6.65159	+	2.16123i	0.311831	+	0.101320i
$456$	−4.32350	+	16.2820i	−0.202466	+	0.762475i
$457$	12.9937	−	17.8843i	0.607820	−	0.836592i	−0.388576	−	0.921417i	$-0.627033\pi$
$457$	12.9937	−	17.8843i	0.607820	−	0.836592i	0.996396	+	0.0848243i	$0.0270329\pi$
$458$	35.6626	+	6.90435i	1.66641	+	0.322619i
$459$	3.61107	−	1.17331i	0.168550	−	0.0547653i
$460$	−7.72587	+	9.23544i	−0.360221	+	0.430605i
$461$	−19.6830			−0.916730			−0.458365	−	0.888764i	$-0.651565\pi$
$461$	−19.6830			−0.916730			−0.458365	+	0.888764i	$0.651565\pi$
$462$	−7.67007	−	1.08335i	−0.356844	−	0.0504018i
$463$		−	10.6767i		−	0.496188i	−0.968736	−	0.248094i	$-0.920196\pi$
$463$		−	10.6767i		−	0.496188i	0.968736	−	0.248094i	$-0.0798041\pi$
$464$	7.51445	−	15.5250i	0.348850	−	0.720729i
$465$	−1.50045	−	4.61790i	−0.0695815	−	0.214150i
$466$	33.3203	+	6.45087i	1.54353	+	0.298831i
$467$	−26.3995	−	19.1804i	−1.22162	−	0.887562i	−0.225391	−	0.974268i	$-0.572366\pi$
$467$	−26.3995	−	19.1804i	−1.22162	−	0.887562i	−0.996234	+	0.0867060i	$0.972366\pi$
$468$	−11.2844	−	4.53952i	−0.521623	−	0.209839i
$469$	−5.46728	+	16.8266i	−0.252456	+	0.776979i
$470$	−2.32205	−	4.96991i	−0.107108	−	0.229245i
$471$	−3.91348	−	5.38645i	−0.180324	−	0.248194i
$472$	−32.2810	+	12.4749i	−1.48585	+	0.574206i
$473$	−26.2490	+	21.1935i	−1.20693	+	0.974480i
$474$	−4.80431	+	0.593554i	−0.220669	+	0.0272628i
$475$	15.8069	+	21.7563i	0.725269	+	0.998247i
$476$	−10.6255	+	6.66174i	−0.487019	+	0.305340i
$477$	−4.17249	−	1.35572i	−0.191045	−	0.0620743i
$478$	19.7564	+	10.9318i	0.903637	+	0.500008i
$479$	12.8754	+	9.35454i	0.588293	+	0.427420i	0.841704	−	0.539939i	$-0.181553\pi$
$479$	12.8754	+	9.35454i	0.588293	+	0.427420i	−0.253411	+	0.967359i	$0.581553\pi$
$480$	3.76262	−	1.16580i	0.171739	−	0.0532113i
$481$	12.3055	−	3.99829i	0.561082	−	0.182306i
$482$	9.09992	+	9.74380i	0.414490	+	0.443818i
$483$			14.2786i			0.649697i
$484$	21.1394	+	6.09315i	0.960881	+	0.276961i
$485$			3.00021i			0.136232i
$486$	−1.03357	+	0.965267i	−0.0468835	+	0.0437854i
$487$	36.0858	−	11.7250i	1.63520	−	0.531310i	0.659744	−	0.751490i	$-0.270665\pi$
$487$	36.0858	−	11.7250i	1.63520	−	0.531310i	0.975459	+	0.220180i	$0.0706645\pi$
$488$	0.0457332	+	0.836609i	0.00207025	+	0.0378715i
$489$	0.612537	+	0.445034i	0.0276999	+	0.0201251i
$490$	2.03708	−	3.68149i	0.0920257	−	0.166313i
$491$	0.524914	+	0.170555i	0.0236890	+	0.00769703i	0.320838	−	0.947134i	$-0.396036\pi$
$491$	0.524914	+	0.170555i	0.0236890	+	0.00769703i	−0.297149	+	0.954831i	$0.596036\pi$
$492$	−1.31290	+	0.823134i	−0.0591902	+	0.0371098i
$493$	9.62334	+	13.2454i	0.433414	+	0.596543i
$494$	6.28108	+	50.8399i	0.282599	+	2.28740i
$495$	−1.79690	+	1.45083i	−0.0807649	+	0.0652099i
$496$	−13.1683	−	24.5876i	−0.591273	−	1.10402i
$497$	1.88343	+	2.59232i	0.0844835	+	0.116282i
$498$	4.16091	−	1.94407i	0.186455	−	0.0871157i
$499$	0.743321	−	2.28771i	0.0332756	−	0.102412i	−0.933039	−	0.359775i	$-0.882854\pi$
$499$	0.743321	−	2.28771i	0.0332756	−	0.102412i	0.966315	+	0.257363i	$0.0828536\pi$
$500$	4.94565	−	12.2940i	0.221176	−	0.549804i
$501$	11.1349	+	8.08998i	0.497471	+	0.361434i
$502$	−1.06453	+	5.49855i	−0.0475123	+	0.245412i
$503$	−0.451670	−	1.39010i	−0.0201390	−	0.0619814i	0.940482	−	0.339844i	$-0.110374\pi$
$503$	−0.451670	−	1.39010i	−0.0201390	−	0.0619814i	−0.960621	+	0.277862i	$0.910374\pi$
$504$	2.53526	−	3.92326i	0.112929	−	0.174756i
$505$			3.63114i			0.161584i
$506$	5.67149	−	40.1540i	0.252128	−	1.78506i
$507$	−23.9864			−1.06527
$508$	−8.16653	+	9.76221i	−0.362331	+	0.433128i
$509$	−38.7738	+	12.5984i	−1.71862	+	0.558413i	−0.991730	−	0.128342i	$-0.959035\pi$
$509$	−38.7738	+	12.5984i	−1.71862	+	0.558413i	−0.726889	+	0.686755i	$0.759035\pi$
$510$	−0.710697	+	3.67092i	−0.0314702	+	0.162551i
$511$	−7.05278	+	9.70732i	−0.311997	+	0.429427i
$512$	20.0914	−	10.4085i	0.887921	−	0.459996i
$513$	5.66454	+	1.84052i	0.250096	+	0.0812610i
$514$	−12.1433	−	25.9906i	−0.535620	−	1.14639i
$515$	−1.95367	+	1.41942i	−0.0860890	+	0.0625473i
$516$	−4.95130	−	19.7324i	−0.217969	−	0.868670i
$517$	15.4800	+	10.0845i	0.680809	+	0.443517i
$518$	0.609261	+	4.93145i	0.0267694	+	0.216675i
$519$	3.55765	−	2.58478i	0.156163	−	0.113459i
$520$	9.29171	−	7.55897i	0.407469	−	0.331483i
$521$	−0.971088	+	2.98870i	−0.0425441	+	0.130937i	−0.970073	−	0.242815i	$-0.921929\pi$
$521$	−0.971088	+	2.98870i	−0.0425441	+	0.130937i	0.927528	+	0.373753i	$0.121929\pi$
$522$	−5.33571	−	2.95240i	−0.233538	−	0.129223i
$523$	2.82713	−	3.89121i	0.123622	−	0.170151i	−0.742720	−	0.669602i	$-0.766465\pi$
$523$	2.82713	−	3.89121i	0.123622	−	0.170151i	0.866342	+	0.499451i	$0.166465\pi$
$524$	0.478345	+	0.0327280i	0.0208966	+	0.00142973i
$525$	−2.30424	−	7.09173i	−0.100565	−	0.309508i
$526$	5.02831	−	4.69603i	0.219245	−	0.204757i
$527$	26.4757			1.15330
$528$	−8.68796	+	10.0259i	−0.378095	+	0.436323i
$529$	−51.7505			−2.25002
$530$	3.15753	−	2.94888i	0.137155	−	0.128091i
$531$	3.78102	+	11.6368i	0.164082	+	0.504993i
$532$	−19.6269	−	1.34286i	−0.850934	−	0.0582202i
$533$	−2.76968	+	3.81214i	−0.119968	+	0.165122i
$534$	8.20710	+	4.54122i	0.355156	+	0.196518i
$535$	−1.78331	+	5.48846i	−0.0770991	+	0.237287i
$536$	19.1220	+	23.5053i	0.825944	+	1.01528i
$537$	−13.6993	+	9.95311i	−0.591167	+	0.429508i
$538$	−5.00667	−	40.5247i	−0.215853	−	1.74714i
$539$	0.721261	+	14.1521i	0.0310669	+	0.609575i
$540$	−0.338947	−	1.35080i	−0.0145859	−	0.0581293i
$541$	−12.8453	+	9.33268i	−0.552264	+	0.401243i	−0.828620	−	0.559812i	$-0.810873\pi$
$541$	−12.8453	+	9.33268i	−0.552264	+	0.401243i	0.276355	+	0.961056i	$0.410873\pi$
$542$	8.75309	+	18.7343i	0.375977	+	0.804709i
$543$	−17.4500	−	5.66985i	−0.748851	−	0.243316i
$544$	−0.294291	+	21.4765i	−0.0126176	+	0.920798i
$545$	−7.27656	+	10.0153i	−0.311693	+	0.429009i
$546$	2.69981	−	13.9451i	0.115541	−	0.596797i
$547$	2.96072	−	0.961995i	0.126591	−	0.0411319i	−0.245036	−	0.969514i	$-0.578800\pi$
$547$	2.96072	−	0.961995i	0.126591	−	0.0411319i	0.371627	+	0.928382i	$0.378800\pi$
$548$	−3.79763	+	4.53966i	−0.162227	+	0.193925i
$549$	0.296228			0.0126427
$550$	3.66311	+	20.8585i	0.156196	+	0.889411i
$551$			25.6824i			1.09411i
$552$	20.5389	+	13.2725i	0.874193	+	0.564914i
$553$	−1.74689	−	5.37637i	−0.0742852	−	0.228626i
$554$	−7.43134	+	38.3846i	−0.315727	+	1.63081i
$555$	1.19853	+	0.870785i	0.0508749	+	0.0369627i
$556$	1.17879	−	2.93025i	0.0499917	−	0.124270i
$557$	−1.84128	+	5.66686i	−0.0780174	+	0.240113i	−0.982457	−	0.186489i	$-0.940289\pi$
$557$	−1.84128	+	5.66686i	−0.0780174	+	0.240113i	0.904440	+	0.426601i	$0.140289\pi$
$558$	−8.93420	+	4.17425i	−0.378215	+	0.176710i
$559$	−36.3620	−	50.0480i	−1.53795	−	2.11681i
$560$	2.17175	+	4.05506i	0.0917732	+	0.171358i
$561$	−4.49597	−	11.7630i	−0.189820	−	0.496633i
$562$	4.97874	+	40.2986i	0.210016	+	1.69989i
$563$	−11.7180	−	16.1284i	−0.493853	−	0.679730i	0.487240	−	0.873268i	$-0.338004\pi$
$563$	−11.7180	−	16.1284i	−0.493853	−	0.679730i	−0.981093	+	0.193538i	$0.938004\pi$
$564$	−9.43913	+	5.91793i	−0.397459	+	0.249190i
$565$	−4.94033	−	1.60521i	−0.207841	−	0.0675317i
$566$	10.7525	−	19.4324i	0.451960	−	0.816803i
$567$	−1.33609	−	0.970725i	−0.0561104	−	0.0407666i
$568$	5.47963	−	0.299544i	0.229920	−	0.0125686i
$569$	−10.2471	+	3.32949i	−0.429582	+	0.139580i	−0.515824	−	0.856695i	$-0.672514\pi$
$569$	−10.2471	+	3.32949i	−0.429582	+	0.139580i	0.0862422	+	0.996274i	$0.472514\pi$
$570$	−4.28665	+	4.00338i	−0.179548	+	0.167683i
$571$			31.9637i			1.33764i	0.743424	+	0.668820i	$0.233200\pi$
$571$			31.9637i			1.33764i	−0.743424	+	0.668820i	$0.766800\pi$
$572$	−13.1314	+	38.1440i	−0.549052	+	1.59488i
$573$			24.8068i			1.03632i
$574$	−1.23514	−	1.32253i	−0.0515536	−	0.0552013i
$575$	37.1263	−	12.0631i	1.54827	−	0.503065i
$576$	−3.28676	−	7.29364i	−0.136948	−	0.303902i
$577$	−0.0764768	−	0.0555637i	−0.00318377	−	0.00231315i	0.586192	−	0.810172i	$-0.300626\pi$
$577$	−0.0764768	−	0.0555637i	−0.00318377	−	0.00231315i	−0.589376	+	0.807859i	$0.700626\pi$
$578$	3.19688	+	1.76892i	0.132973	+	0.0735775i
$579$	−0.0223345	−	0.00725691i	−0.000928189	−	0.000301587i
$580$	5.08793	−	3.18992i	0.211265	−	0.132454i
$581$	3.15243	+	4.33895i	0.130785	+	0.180010i
$582$	6.04722	−	0.747111i	0.250665	−	0.0309687i
$583$	−3.78623	+	14.0495i	−0.156810	+	0.581871i
$584$	7.40758	+	19.1684i	0.306528	+	0.793192i
$585$	−2.48920	−	3.42609i	−0.102916	−	0.141652i
$586$	−11.5777	−	24.7798i	−0.478269	−	1.02365i
$587$	−1.27747	+	3.93166i	−0.0527270	+	0.162277i	−0.973953	−	0.226752i	$-0.927189\pi$
$587$	−1.27747	+	3.93166i	−0.0527270	+	0.162277i	0.921226	+	0.389029i	$0.127189\pi$
$588$	−7.92770	−	3.18917i	−0.326933	−	0.131519i
$589$	33.5995	+	24.4115i	1.38444	+	1.00586i
$590$	−11.8296	−	2.29024i	−0.487019	−	0.0942878i
$591$	0.0566906	+	0.174476i	0.00233194	+	0.00717697i
$592$	7.65993	+	3.70758i	0.314821	+	0.152381i
$593$		−	35.7489i		−	1.46803i	−0.679133	−	0.734015i	$-0.737644\pi$
$593$		−	35.7489i		−	1.46803i	0.679133	−	0.734015i	$-0.262356\pi$
$594$	3.37176	+	3.26056i	0.138345	+	0.133782i
$595$	−4.36644			−0.179007
$596$	23.4478	−	28.0293i	0.960460	−	1.14813i
$597$	−14.0786	+	4.57441i	−0.576198	+	0.187218i
$598$	73.0050	+	14.1339i	2.98540	+	0.577978i
$599$	7.34693	−	10.1122i	0.300187	−	0.413172i	−0.632102	−	0.774885i	$-0.717808\pi$
$599$	7.34693	−	10.1122i	0.300187	−	0.413172i	0.932290	+	0.361713i	$0.117808\pi$
$600$	−12.3429	−	3.27752i	−0.503898	−	0.133804i
$601$	21.8025	+	7.08405i	0.889341	+	0.288964i	0.717830	−	0.696218i	$-0.245135\pi$
$601$	21.8025	+	7.08405i	0.889341	+	0.288964i	0.171510	+	0.985182i	$0.445135\pi$
$602$	21.5241	−	10.0565i	0.877255	−	0.409872i
$603$	8.66701	−	6.29695i	0.352948	−	0.256432i
$604$	29.4239	−	7.38311i	1.19724	−	0.300415i
$605$	5.10895	+	5.70702i	0.207709	+	0.232023i
$606$	7.31894	−	0.904227i	0.297312	−	0.0367317i
$607$	23.1519	−	16.8209i	0.939708	−	0.682738i	−0.00864207	−	0.999963i	$-0.502751\pi$
$607$	23.1519	−	16.8209i	0.939708	−	0.682738i	0.948350	+	0.317225i	$0.102751\pi$
$608$	−20.1756	+	26.9839i	−0.818228	+	1.09434i
$609$	2.20058	−	6.77269i	0.0891720	−	0.274443i
$610$	−0.141236	+	0.255247i	−0.00571846	+	0.0103347i
$611$	−19.9126	+	27.4074i	−0.805579	+	1.10878i
$612$	7.57610	+	0.518350i	0.306246	+	0.0209531i
$613$	4.21216	+	12.9637i	0.170128	+	0.523599i	0.999378	−	0.0352789i	$-0.0112320\pi$
$613$	4.21216	+	12.9637i	0.170128	+	0.523599i	−0.829250	+	0.558878i	$0.811232\pi$
$614$	−17.2739	−	18.4962i	−0.697119	−	0.746445i
$615$	−0.539524			−0.0217557
$616$	−13.4231	−	7.73531i	−0.540832	−	0.311664i
$617$	14.0298			0.564819			0.282410	−	0.959294i	$-0.408866\pi$
$617$	14.0298			0.564819			0.282410	+	0.959294i	$0.408866\pi$
$618$	3.34750	+	3.58436i	0.134656	+	0.144184i
$619$	−7.23719	−	22.2738i	−0.290887	−	0.895259i	−0.984572	−	0.174980i	$-0.944014\pi$
$619$	−7.23719	−	22.2738i	−0.290887	−	0.895259i	0.693685	−	0.720279i	$-0.255986\pi$
$620$	0.662875	−	9.68844i	0.0266217	−	0.389097i
$621$	5.08190	−	6.99463i	0.203929	−	0.280685i
$622$	−0.677353	+	1.22414i	−0.0271594	+	0.0490836i
$623$	−3.38481	+	10.4174i	−0.135610	+	0.417364i
$624$	−17.5497	−	16.8461i	−0.702550	−	0.674382i
$625$	−14.5314	+	10.5577i	−0.581256	+	0.422307i
$626$	−18.9465	+	2.34077i	−0.757256	+	0.0935561i
$627$	5.14016	−	19.0735i	0.205278	−	0.761723i
$628$	−3.24082	−	12.9156i	−0.129323	−	0.515390i
$629$	−6.53520	+	4.74810i	−0.260575	+	0.189319i
$630$	1.47345	−	0.688429i	0.0587038	−	0.0274277i
$631$	16.4648	+	5.34974i	0.655453	+	0.212970i	0.617817	−	0.786322i	$-0.288017\pi$
$631$	16.4648	+	5.34974i	0.655453	+	0.212970i	0.0376362	+	0.999292i	$0.488017\pi$
$632$	−9.35739	−	2.48475i	−0.372217	−	0.0988379i
$633$	−6.77305	+	9.32230i	−0.269205	+	0.370528i
$634$	−12.2751	−	2.37648i	−0.487505	−	0.0943819i
$635$	−4.21449	+	1.36937i	−0.167247	+	0.0543418i
$636$	−6.73006	−	5.63000i	−0.266864	−	0.223244i
$637$	−25.9842			−1.02953
$638$	−8.87859	+	18.1720i	−0.351507	+	0.719437i
$639$		−	1.94023i		−	0.0767545i
$640$	7.85170	+	0.645403i	0.310366	+	0.0255118i
$641$	−0.223394	−	0.687535i	−0.00882352	−	0.0271560i	0.946548	−	0.322564i	$-0.104545\pi$
$641$	−0.223394	−	0.687535i	−0.00882352	−	0.0271560i	−0.955371	+	0.295407i	$0.904545\pi$
$642$	11.5066	+	2.22770i	0.454130	+	0.0879205i
$643$	3.53380	+	2.56746i	0.139359	+	0.101251i	0.655281	−	0.755385i	$-0.272550\pi$
$643$	3.53380	+	2.56746i	0.139359	+	0.101251i	−0.515921	+	0.856636i	$0.672550\pi$
$644$	−10.6579	+	26.4937i	−0.419982	+	1.04400i
$645$	2.18883	−	6.73652i	0.0861850	−	0.265250i
$646$	−13.5378	−	28.9752i	−0.532639	−	1.14002i
$647$	19.5634	+	26.9267i	0.769115	+	1.05860i	0.996401	+	0.0847680i	$0.0270149\pi$
$647$	19.5634	+	26.9267i	0.769115	+	1.05860i	−0.227286	+	0.973828i	$0.572985\pi$
$648$	−2.63828	+	1.01956i	−0.103641	+	0.0400520i
$649$	37.9065	−	14.4884i	1.48796	−	0.568719i
$650$	−38.5403	+	4.76151i	−1.51167	+	0.186762i
$651$	−6.76882	−	9.31649i	−0.265291	−	0.365142i
$652$	0.804369	+	1.28297i	0.0315015	+	0.0502451i
$653$	14.5362	+	4.72309i	0.568845	+	0.184829i	0.579297	−	0.815116i	$-0.303327\pi$
$653$	14.5362	+	4.72309i	0.568845	+	0.184829i	−0.0104521	+	0.999945i	$0.503327\pi$
$654$	21.9989	+	12.1726i	0.860225	+	0.475987i
$655$	0.135053	+	0.0981217i	0.00527695	+	0.00383393i
$656$	−3.05049	+	0.547328i	−0.119102	+	0.0213696i
$657$	6.90989	−	2.24516i	0.269580	−	0.0875920i
$658$	−8.88002	−	9.50835i	−0.346179	−	0.370674i
$659$		−	31.0396i		−	1.20913i	−0.796556	−	0.604565i	$-0.793347\pi$
$659$		−	31.0396i		−	1.20913i	0.796556	−	0.604565i	$-0.206653\pi$
$660$	−4.41708	+	1.35073i	−0.171935	+	0.0525772i
$661$		−	30.3454i		−	1.18030i	−0.807294	−	0.590149i	$-0.799069\pi$
$661$		−	30.3454i		−	1.18030i	0.807294	−	0.590149i	$-0.200931\pi$
$662$	9.35529	−	8.73708i	0.363604	−	0.339576i
$663$	21.9612	−	7.13564i	0.852904	−	0.277125i
$664$	9.17163	−	0.501367i	0.355928	−	0.0194568i
$665$	−5.54133	−	4.02601i	−0.214884	−	0.156122i
$666$	1.45670	−	2.63261i	0.0564459	−	0.102011i
$667$	35.4561	+	11.5204i	1.37287	+	0.446071i
$668$	14.6221	+	23.3223i	0.565746	+	0.902367i
$669$	−5.95380	−	8.19470i	−0.230187	−	0.316826i
$670$	1.29356	+	10.4703i	0.0499747	+	0.404502i
$671$	−0.0500069	−	0.981203i	−0.00193049	−	0.0378789i
$672$	7.63258	−	5.38717i	0.294433	−	0.207815i
$673$	8.88632	+	12.2310i	0.342543	+	0.471469i	0.945182	−	0.326544i	$-0.105884\pi$
$673$	8.88632	+	12.2310i	0.342543	+	0.471469i	−0.602639	+	0.798014i	$0.705884\pi$
$674$	−17.4968	+	8.17486i	−0.673950	+	0.314884i
$675$	−1.39525	+	4.29413i	−0.0537031	+	0.165281i
$676$	−44.5065	−	17.9041i	−1.71179	−	0.688621i
$677$	−29.0399	−	21.0987i	−1.11609	−	0.810890i	−0.132482	−	0.991185i	$-0.542295\pi$
$677$	−29.0399	−	21.0987i	−1.11609	−	0.810890i	−0.983613	+	0.180295i	$0.942295\pi$
$678$	−2.00523	+	10.3575i	−0.0770102	+	0.397776i
$679$	2.19882	+	6.76728i	0.0843830	+	0.259704i
$680$	−4.05878	+	6.28087i	−0.155647	+	0.240860i
$681$			9.22135i			0.353363i
$682$	15.3347	+	28.8883i	0.587195	+	1.10619i
$683$	16.5721			0.634112			0.317056	−	0.948407i	$-0.397306\pi$
$683$	16.5721			0.634112			0.317056	+	0.948407i	$0.397306\pi$
$684$	9.13668	+	7.64325i	0.349350	+	0.292247i
$685$	−1.95984	+	0.636790i	−0.0748816	+	0.0243305i
$686$	5.00420	−	25.8479i	0.191061	−	0.986876i
$687$	15.0976	−	20.7800i	0.576009	−	0.792808i
$688$	5.54176	−	40.3090i	0.211278	−	1.53677i
$689$	−25.3756	−	8.24503i	−0.966733	−	0.314111i
$690$	3.60404	+	7.71377i	0.137203	+	0.293658i
$691$	17.4532	−	12.6805i	0.663949	−	0.482387i	−0.204045	−	0.978961i	$-0.565409\pi$
$691$	17.4532	−	12.6805i	0.663949	−	0.482387i	0.867994	+	0.496574i	$0.165409\pi$
$692$	8.53054	−	2.14050i	0.324283	−	0.0813697i
$693$	−2.98981	+	4.58943i	−0.113573	+	0.174338i
$694$	−0.404385	−	3.27315i	−0.0153503	−	0.124247i
$695$	0.889662	−	0.646377i	0.0337468	−	0.0245185i
$696$	−7.69660	−	9.46089i	−0.291739	−	0.358614i
$697$	0.909080	−	2.79786i	0.0344338	−	0.105976i
$698$	−18.0050	−	9.96267i	−0.681498	−	0.377093i
$699$	14.1060	−	19.4152i	0.533536	−	0.734350i
$700$	1.01798	−	14.8786i	0.0384760	−	0.562358i
$701$	−10.2401	−	31.5157i	−0.386762	−	1.19033i	−0.935194	−	0.354135i	$-0.884775\pi$
$701$	−10.2401	−	31.5157i	−0.386762	−	1.19033i	0.548432	−	0.836195i	$-0.315225\pi$
$702$	−6.28578	+	5.87041i	−0.237242	+	0.221564i
$703$	−12.6716			−0.477917
$704$	−23.6041	+	12.1181i	−0.889612	+	0.456717i
$705$	−3.87891			−0.146088
$706$	24.5401	−	22.9185i	0.923580	−	0.862549i
$707$	2.66123	+	8.19043i	0.100086	+	0.308033i
$708$	−1.67040	+	24.4142i	−0.0627774	+	0.917541i
$709$	11.7145	−	16.1236i	0.439946	−	0.605534i	−0.530254	−	0.847839i	$-0.677903\pi$
$709$	11.7145	−	16.1236i	0.439946	−	0.605534i	0.970200	+	0.242305i	$0.0779035\pi$
$710$	1.67182	+	0.925066i	0.0627423	+	0.0347171i
$711$	−1.05776	+	3.25545i	−0.0396692	+	0.122089i
$712$	11.8385	+	14.5522i	0.443666	+	0.545368i
$713$	48.7733	−	35.4359i	1.82657	−	1.32708i
$714$	1.08733	+	8.80101i	0.0406924	+	0.329370i
$715$	−10.9281	+	8.82342i	−0.408689	+	0.329977i
$716$	−32.8482	+	8.24234i	−1.22759	+	0.308031i
$717$	12.9167	−	9.38451i	0.482382	−	0.350471i
$718$	−6.33719	−	13.5636i	−0.236502	−	0.506188i
$719$	−8.25695	−	2.68285i	−0.307932	−	0.100053i	0.150974	−	0.988538i	$-0.451759\pi$
$719$	−8.25695	−	2.68285i	−0.307932	−	0.100053i	−0.458907	+	0.888484i	$0.651759\pi$
$720$	0.379367	−	2.75940i	0.0141382	−	0.102837i
$721$	−3.36642	+	4.63348i	−0.125372	+	0.172560i
$722$	4.42841	−	22.8738i	0.164808	−	0.851275i
$723$	8.96595	−	2.91321i	0.333447	−	0.108344i
$724$	−28.1462	−	23.5455i	−1.04604	−	0.875063i
$725$	−19.4691			−0.723065
$726$	10.2308	−	11.7188i	0.379702	−	0.434925i
$727$			8.14327i			0.302017i	0.988532	+	0.151009i	$0.0482521\pi$
$727$			8.14327i			0.302017i	−0.988532	+	0.151009i	$0.951748\pi$
$728$	15.4185	−	23.8599i	0.571449	−	0.884305i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−1.35994	+	7.02441i	−0.0503336	+	0.259985i
$731$	31.2461	+	22.7016i	1.15568	+	0.839649i
$732$	0.549647	+	0.221113i	0.0203156	+	0.00817258i
$733$	−0.185339	+	0.570415i	−0.00684566	+	0.0210688i	−0.954421	−	0.298464i	$-0.903526\pi$
$733$	−0.185339	+	0.570415i	−0.00684566	+	0.0210688i	0.947575	+	0.319532i	$0.103526\pi$
$734$	33.4320	−	15.6201i	1.23400	−	0.576549i
$735$	−1.74875	−	2.40695i	−0.0645036	−	0.0887816i
$736$	28.2027	+	39.9578i	1.03957	+	1.47286i
$737$	−22.3207	−	27.6450i	−0.822192	−	1.01832i
$738$	0.134352	+	1.08747i	0.00494557	+	0.0400302i
$739$	3.55308	+	4.89040i	0.130702	+	0.179896i	0.869352	−	0.494193i	$-0.164536\pi$
$739$	3.55308	+	4.89040i	0.130702	+	0.179896i	−0.738650	+	0.674089i	$0.764536\pi$
$740$	1.57388	+	2.51035i	0.0578571	+	0.0922824i
$741$	34.4497	+	11.1934i	1.26554	+	0.411200i
$742$	4.96094	−	8.96563i	0.182122	−	0.329139i
$743$	−14.7479	−	10.7149i	−0.541046	−	0.393093i	0.283427	−	0.958994i	$-0.408529\pi$
$743$	−14.7479	−	10.7149i	−0.541046	−	0.393093i	−0.824473	+	0.565901i	$0.808529\pi$
$744$	−19.6931	+	1.07652i	−0.721984	+	0.0394672i
$745$	12.1007	−	3.93175i	0.443335	−	0.144048i
$746$	17.2776	−	16.1359i	0.632579	−	0.590778i
$747$		−	3.24750i		−	0.118820i
$748$	0.438006	−	25.1820i	0.0160151	−	0.920745i
$749$			13.6868i			0.500103i
$750$	−6.39561	−	6.84815i	−0.233535	−	0.250059i
$751$	−48.5455	+	15.7734i	−1.77145	+	0.575579i	−0.998280	−	0.0586211i	$-0.981330\pi$
$751$	−48.5455	+	15.7734i	−1.77145	+	0.575579i	−0.773169	+	0.634200i	$0.781330\pi$
$752$	−21.9315	+	3.93502i	−0.799761	+	0.143495i
$753$	3.20392	+	2.32778i	0.116757	+	0.0848290i
$754$	−32.4499	−	17.9555i	−1.18176	−	0.653899i
$755$	10.0451	+	3.26386i	0.365580	+	0.118784i
$756$	−1.75452	−	2.79847i	−0.0638113	−	0.101779i
$757$	4.99944	+	6.88113i	0.181708	+	0.250099i	0.890148	−	0.455672i	$-0.150601\pi$
$757$	4.99944	+	6.88113i	0.181708	+	0.250099i	−0.708440	+	0.705771i	$0.750601\pi$
$758$	−35.1737	+	4.34557i	−1.27757	+	0.157838i
$759$	−24.0264	−	15.6521i	−0.872102	−	0.568136i
$760$	−10.9421	+	4.22855i	−0.396911	+	0.153386i
$761$	20.9441	+	28.8271i	0.759224	+	1.04498i	0.997278	+	0.0737302i	$0.0234904\pi$
$761$	20.9441	+	28.8271i	0.759224	+	1.04498i	−0.238054	+	0.971252i	$0.576510\pi$
$762$	3.80960	+	8.15374i	0.138007	+	0.295379i
$763$	−9.07290	+	27.9235i	−0.328461	+	1.01090i
$764$	−18.5166	+	46.0288i	−0.669905	+	1.66526i
$765$	2.13899	+	1.55406i	0.0773352	+	0.0561873i
$766$	−12.1498	−	2.35222i	−0.438990	−	0.0849893i
$767$	22.9948	+	70.7707i	0.830294	+	2.55538i
$768$	−0.654354	−	15.9866i	−0.0236120	−	0.576867i
$769$			45.0073i			1.62300i	0.584350	+	0.811502i	$0.301349\pi$
$769$			45.0073i			1.62300i	−0.584350	+	0.811502i	$0.698651\pi$
$770$	−2.52904	−	4.76435i	−0.0911403	−	0.171695i
$771$	−20.2851			−0.730550
$772$	−0.0360246	−	0.0301362i	−0.00129655	−	0.00108463i
$773$	−27.7270	+	9.00903i	−0.997269	+	0.324032i	−0.761774	−	0.647843i	$-0.775671\pi$
$773$	−27.7270	+	9.00903i	−0.997269	+	0.324032i	−0.235495	+	0.971875i	$0.575671\pi$
$774$	−14.1232	−	2.73428i	−0.507648	−	0.0982816i
$775$	−18.5056	+	25.4708i	−0.664743	+	0.914940i
$776$	11.7782	+	3.12757i	0.422814	+	0.112273i
$777$	3.34160	+	1.08575i	0.119879	+	0.0389512i
$778$	28.9636	−	13.5324i	1.03840	−	0.485161i
$779$	3.73341	−	2.71248i	0.133763	−	0.0971848i
$780$	−2.06135	−	8.21510i	−0.0738082	−	0.294148i
$781$	−6.42669	+	0.327535i	−0.229965	+	0.0117201i
$782$	−46.0747	+	5.69235i	−1.64763	+	0.203558i
$783$	−3.48847	+	2.53452i	−0.124668	+	0.0905765i
$784$	−12.3293	−	11.8349i	−0.440331	−	0.422676i
$785$	1.43268	−	4.40932i	0.0511344	−	0.157375i
$786$	0.164143	−	0.296647i	0.00585480	−	0.0105811i
$787$	16.0741	−	22.1241i	0.572980	−	0.788639i	−0.419924	−	0.907559i	$-0.637943\pi$
$787$	16.0741	−	22.1241i	0.572980	−	0.788639i	0.992904	+	0.118920i	$0.0379432\pi$
$788$	−0.0250451	+	0.366053i	−0.000892193	+	0.0130401i
$789$	−1.50337	−	4.62690i	−0.0535214	−	0.164722i
$790$	−2.30077	−	2.46357i	−0.0818578	−	0.0876498i
$791$	−12.3199			−0.438044
$792$	3.82248	+	8.56672i	0.135826	+	0.304405i
$793$	1.80155			0.0639749
$794$	−2.68861	−	2.87885i	−0.0954153	−	0.102167i
$795$	−0.944044	−	2.90547i	−0.0334818	−	0.103046i
$796$	−29.5371	−	2.02091i	−1.04692	−	0.0716291i
$797$	−0.554736	+	0.763529i	−0.0196498	+	0.0270456i	−0.818729	−	0.574180i	$-0.805321\pi$
$797$	−0.554736	+	0.763529i	−0.0196498	+	0.0270456i	0.799079	+	0.601226i	$0.205321\pi$
$798$	−6.73494	+	12.1717i	−0.238414	+	0.430873i
$799$	6.53584	−	20.1152i	0.231221	−	0.711626i
$800$	−20.4557	−	15.2945i	−0.723219	−	0.540743i
$801$	5.36578	−	3.89847i	0.189590	−	0.137746i
$802$	9.00432	−	1.11245i	0.317954	−	0.0392820i
$803$	−8.60317	−	22.5088i	−0.303599	−	0.794318i
$804$	20.7818	−	5.21462i	0.732917	−	0.183905i
$805$	−8.04383	+	5.84418i	−0.283508	+	0.205980i
$806$	−54.3346	+	25.3863i	−1.91386	+	0.894194i
$807$	−27.4600	−	8.92229i	−0.966638	−	0.314080i
$808$	14.2552	+	3.78529i	0.501495	+	0.133166i
$809$	11.5315	−	15.8717i	0.405424	−	0.558019i	−0.556671	−	0.830733i	$-0.687921\pi$
$809$	11.5315	−	15.8717i	0.405424	−	0.558019i	0.962095	+	0.272714i	$0.0879214\pi$
$810$	−0.966820	−	0.187178i	−0.0339706	−	0.00657677i
$811$	−18.2649	+	5.93462i	−0.641367	+	0.208393i	−0.611604	−	0.791164i	$-0.709475\pi$
$811$	−18.2649	+	5.93462i	−0.641367	+	0.208393i	−0.0297632	+	0.999557i	$0.509475\pi$
$812$	9.13850	−	10.9241i	0.320698	−	0.383360i
$813$	14.6218			0.512808
$814$	−8.96596	−	4.38064i	−0.314257	−	0.153541i
$815$			0.527224i			0.0184679i
$816$	13.6705	+	6.61682i	0.478562	+	0.231635i
$817$	18.7219	+	57.6200i	0.654995	+	2.01587i
$818$	−41.4415	−	8.02314i	−1.44897	−	0.280523i
$819$	−8.12561	−	5.90360i	−0.283932	−	0.206288i
$820$	−1.00108	−	0.402717i	−0.0349593	−	0.0140635i
$821$	4.88277	−	15.0276i	0.170410	−	0.524467i	−0.828984	−	0.559272i	$-0.811081\pi$
$821$	4.88277	−	15.0276i	0.170410	−	0.524467i	0.999394	+	0.0348046i	$0.0110809\pi$
$822$	1.77155	+	3.79168i	0.0617901	+	0.132250i
$823$	−23.2795	−	32.0414i	−0.811471	−	1.11689i	−0.991095	−	0.133159i	$-0.957488\pi$
$823$	−23.2795	−	32.0414i	−0.811471	−	1.11689i	0.179623	−	0.983735i	$-0.442512\pi$
$824$	3.53578	+	9.14941i	0.123175	+	0.318735i
$825$	14.4591	+	3.89661i	0.503401	+	0.135663i
$826$	−28.3615	+	3.50396i	−0.986823	+	0.121918i
$827$	−23.2594	−	32.0138i	−0.808807	−	1.11323i	−0.991506	−	0.130058i	$-0.958484\pi$
$827$	−23.2594	−	32.0138i	−0.808807	−	1.11323i	0.182699	−	0.983169i	$-0.441516\pi$
$828$	14.6504	−	9.18519i	0.509137	−	0.319207i
$829$	−14.5137	−	4.71578i	−0.504081	−	0.163786i	0.0459279	−	0.998945i	$-0.485376\pi$
$829$	−14.5137	−	4.71578i	−0.504081	−	0.163786i	−0.550009	+	0.835159i	$0.685376\pi$
$830$	2.79824	+	1.54835i	0.0971283	+	0.0537439i
$831$	22.3661	+	16.2499i	0.775871	+	0.563704i
$832$	−19.9889	−	44.3573i	−0.692990	−	1.53781i
$833$	15.4285	−	5.01303i	0.534567	−	0.173691i
$834$	−1.52438	−	1.63224i	−0.0527851	−	0.0565200i
$835$			9.58406i			0.331670i
$836$	23.7746	−	31.5539i	0.822260	−	1.09132i
$837$			6.97296i			0.241021i
$838$	−2.60605	+	2.43384i	−0.0900244	+	0.0840755i
$839$	13.3878	−	4.34995i	0.462197	−	0.150177i	−0.0686565	−	0.997640i	$-0.521871\pi$
$839$	13.3878	−	4.34995i	0.462197	−	0.150177i	0.530854	+	0.847463i	$0.321871\pi$
$840$	3.24784	−	0.177543i	0.112061	−	0.00612582i
$841$	8.41924	+	6.11693i	0.290318	+	0.210929i
$842$	−20.7730	+	37.5418i	−0.715884	+	1.29378i
$843$	27.3068	+	8.87252i	0.940496	+	0.305586i
$844$	−19.5258	+	12.2418i	−0.672105	+	0.421381i
$845$	−9.81757	−	13.5127i	−0.337735	−	0.464852i
$846$	0.965927	+	7.81835i	0.0332093	+	0.268800i
$847$	15.7064	+	9.12847i	0.539678	+	0.313658i
$848$	−8.28515	−	15.4699i	−0.284513	−	0.531240i
$849$	−9.23059	−	12.7048i	−0.316793	−	0.436028i
$850$	21.9653	−	10.2627i	0.753403	−	0.352006i
$851$	−5.68409	+	17.4938i	−0.194848	+	0.599681i
$852$	1.44825	−	3.60009i	0.0496162	−	0.123337i
$853$	15.7626	+	11.4522i	0.539702	+	0.392117i	0.823974	−	0.566627i	$-0.191752\pi$
$853$	15.7626	+	11.4522i	0.539702	+	0.392117i	−0.284272	+	0.958744i	$0.591752\pi$
$854$	−0.131503	+	0.679247i	−0.00449996	+	0.0232434i
$855$	1.28163	+	3.94444i	0.0438307	+	0.134897i
$856$	19.6876	+	12.7224i	0.672909	+	0.434842i
$857$			22.1714i			0.757359i	0.925528	+	0.378680i	$0.123622\pi$
$857$			22.1714i			0.757359i	−0.925528	+	0.378680i	$0.876378\pi$
$858$	20.5058	+	19.8296i	0.700057	+	0.676970i
$859$	−2.34314			−0.0799470			−0.0399735	−	0.999201i	$-0.512727\pi$
$859$	−2.34314			−0.0799470			−0.0399735	+	0.999201i	$0.512727\pi$
$860$	9.08968	−	10.8657i	0.309956	−	0.370518i
$861$	−1.21695	+	0.395412i	−0.0414736	+	0.0134756i
$862$	6.97757	−	36.0408i	0.237657	−	1.22755i
$863$	−29.5571	+	40.6819i	−1.00614	+	1.38483i	−0.0846518	+	0.996411i	$0.526978\pi$
$863$	−29.5571	+	40.6819i	−1.00614	+	1.38483i	−0.921484	+	0.388416i	$0.873022\pi$
$864$	−5.65632	−	0.0775083i	−0.192432	−	0.00263688i
$865$	2.91228	+	0.946256i	0.0990204	+	0.0321737i
$866$	18.4214	+	39.4277i	0.625986	+	1.33981i
$867$	2.09011	−	1.51855i	0.0709838	−	0.0515727i
$868$	−5.60538	−	22.3391i	−0.190259	−	0.758238i
$869$	10.9617	+	2.95409i	0.371850	+	0.100211i
$870$	−0.520659	−	4.21429i	−0.0176520	−	0.142878i
$871$	52.7097	−	38.2958i	1.78600	−	1.29760i
$872$	31.7327	+	39.0068i	1.07461	+	1.32094i
$873$	1.33141	−	4.09767i	0.0450615	−	0.138685i
$874$	−63.7207	−	35.2585i	−2.15538	−	1.19264i
$875$	6.43177	−	8.85257i	0.217434	−	0.299272i
$876$	14.4971	+	0.991878i	0.489811	+	0.0335124i
$877$	−8.48419	−	26.1117i	−0.286491	−	0.881728i	−0.985948	−	0.167053i	$-0.946575\pi$
$877$	−8.48419	−	26.1117i	−0.286491	−	0.881728i	0.699457	−	0.714675i	$-0.253425\pi$
$878$	14.3767	−	13.4267i	0.485191	−	0.453129i
$879$	−19.3401			−0.652327
$880$	−9.20407	−	0.790768i	−0.310269	−	0.0266568i
$881$	15.6647			0.527756			0.263878	−	0.964556i	$-0.414998\pi$
$881$	15.6647			0.527756			0.263878	+	0.964556i	$0.414998\pi$
$882$	−4.41598	+	4.12416i	−0.148694	+	0.138868i
$883$	14.0543	+	43.2547i	0.472965	+	1.45564i	0.848682	+	0.528903i	$0.177397\pi$
$883$	14.0543	+	43.2547i	0.472965	+	1.45564i	−0.375717	+	0.926735i	$0.622603\pi$
$884$	46.0751	+	3.15242i	1.54967	+	0.106027i
$885$	−5.00802	+	6.89294i	−0.168343	+	0.231704i
$886$	11.2208	+	6.20880i	0.376971	+	0.208589i
$887$	−11.7143	+	36.0529i	−0.393327	+	1.21054i	0.536930	+	0.843627i	$0.319584\pi$
$887$	−11.7143	+	36.0529i	−0.393327	+	1.21054i	−0.930257	+	0.366909i	$0.880416\pi$
$888$	4.66794	−	3.79745i	0.156646	−	0.127434i
$889$	−8.50263	+	6.17752i	−0.285169	+	0.207187i
$890$	0.800849	+	6.48218i	0.0268445	+	0.217283i
$891$	3.09804	−	1.18411i	0.103788	−	0.0396693i
$892$	−4.93044	−	19.6493i	−0.165084	−	0.657907i
$893$	26.8414	−	19.5014i	0.898214	−	0.652591i
$894$	−10.9382	−	23.4111i	−0.365827	−	0.782983i
$895$	−11.2142	−	3.64370i	−0.374848	−	0.121796i
$896$	18.1833	−	4.29866i	0.607462	−	0.143608i
$897$	30.9063	−	42.5388i	1.03193	−	1.42033i
$898$	−4.82835	+	24.9396i	−0.161124	+	0.832245i
$899$	−28.5957	+	9.29131i	−0.953721	+	0.309883i
$900$	−5.79413	+	6.92625i	−0.193138	+	0.230875i
$901$	16.6578			0.554953
$902$	3.57936	−	0.628596i	0.119180	−	0.0209300i
$903$		−	16.7991i		−	0.559039i
$904$	−11.4518	+	17.7214i	−0.380881	+	0.589406i
$905$	−3.94814	−	12.1511i	−0.131241	−	0.403917i
$906$	4.07721	−	21.0598i	0.135456	−	0.699664i
$907$	24.3629	+	17.7007i	0.808957	+	0.587742i	0.913528	−	0.406776i	$-0.133347\pi$
$907$	24.3629	+	17.7007i	0.808957	+	0.587742i	−0.104571	+	0.994517i	$0.533347\pi$
$908$	−6.88309	+	17.1101i	−0.228423	+	0.567819i
$909$	1.61141	−	4.95940i	0.0534470	−	0.164493i
$910$	8.96102	−	4.18678i	0.297055	−	0.138790i
$911$	−21.2777	−	29.2863i	−0.704963	−	0.970298i	−0.999891	−	0.0147785i	$-0.995296\pi$
$911$	−21.2777	−	29.2863i	−0.704963	−	0.970298i	0.294928	−	0.955519i	$-0.404704\pi$
$912$	11.2479	+	21.0019i	0.372454	+	0.695441i
$913$	−10.7568	+	0.548218i	−0.355998	+	0.0181434i
$914$	−3.83327	−	31.0270i	−0.126793	−	1.02628i
$915$	0.121245	+	0.166880i	0.00400825	+	0.00551688i
$916$	43.5242	−	27.2879i	1.43808	−	0.901616i
$917$	0.376538	+	0.122345i	0.0124344	+	0.00404018i
$918$	2.59973	−	4.69834i	0.0858037	−	0.155068i
$919$	−22.9541	−	16.6771i	−0.757184	−	0.550127i	0.140861	−	0.990029i	$-0.455013\pi$
$919$	−22.9541	−	16.6771i	−0.757184	−	0.550127i	−0.898045	+	0.439903i	$0.855013\pi$
$920$	0.929467	+	17.0030i	0.0306436	+	0.560571i
$921$	−17.0196	+	5.53001i	−0.560816	+	0.182220i
$922$	−20.3437	+	18.9994i	−0.669985	+	0.625711i
$923$		−	11.7998i		−	0.388395i
$924$	−8.97324	+	6.28396i	−0.295198	+	0.206727i
$925$		−	9.60594i		−	0.315841i
$926$	−10.3059	−	11.0351i	−0.338671	−	0.362635i
$927$	3.29822	−	1.07166i	0.108328	−	0.0351978i
$928$	−7.21907	−	23.2996i	−0.236978	−	0.764845i
$929$	17.2036	+	12.4992i	0.564433	+	0.410084i	0.833079	−	0.553155i	$-0.186576\pi$
$929$	17.2036	+	12.4992i	0.564433	+	0.410084i	−0.268646	+	0.963239i	$0.586576\pi$
$930$	−6.00831	−	3.32457i	−0.197020	−	0.109017i
$931$	24.2021	+	7.86374i	0.793192	+	0.257724i
$932$	40.6655	−	25.4956i	1.33204	−	0.835135i
$933$	0.581482	+	0.800341i	0.0190368	+	0.0262020i
$934$	−45.7999	+	5.65840i	−1.49862	+	0.185148i
$935$	4.78648	−	7.34737i	0.156535	−	0.240285i
$936$	−16.0451	+	6.20059i	−0.524449	+	0.202673i
$937$	−25.3238	−	34.8552i	−0.827293	−	1.13867i	−0.988421	−	0.151738i	$-0.951513\pi$
$937$	−25.3238	−	34.8552i	−0.827293	−	1.13867i	0.161128	−	0.986934i	$-0.448487\pi$
$938$	10.5913	+	22.6688i	0.345819	+	0.740161i
$939$	−4.17145	+	12.8384i	−0.136130	+	0.418965i
$940$	−7.19728	−	2.89534i	−0.234750	−	0.0944355i
$941$	−7.65773	−	5.56367i	−0.249635	−	0.181370i	0.455930	−	0.890016i	$-0.349307\pi$
$941$	−7.65773	−	5.56367i	−0.249635	−	0.181370i	−0.705565	+	0.708645i	$0.749307\pi$
$942$	−9.24420	−	1.78969i	−0.301192	−	0.0583114i
$943$	−2.07004	−	6.37094i	−0.0674099	−	0.207466i
$944$	−21.3229	+	44.0534i	−0.694001	+	1.43382i
$945$		−	1.15000i		−	0.0374095i
$946$	−6.67265	+	47.2422i	−0.216947	+	1.53598i
$947$	58.1103			1.88833			0.944166	−	0.329471i	$-0.106870\pi$
$947$	58.1103			1.88833			0.944166	+	0.329471i	$0.106870\pi$
$948$	−4.39263	+	5.25092i	−0.142666	+	0.170542i
$949$	42.0235	−	13.6542i	1.36414	−	0.443236i
$950$	37.3381	+	7.22872i	1.21141	+	0.234531i
$951$	−5.19658	+	7.15248i	−0.168511	+	0.231935i
$952$	−4.55181	+	17.1418i	−0.147525	+	0.555569i
$953$	−37.3273	−	12.1284i	−1.20915	−	0.392876i	−0.366030	−	0.930603i	$-0.619283\pi$
$953$	−37.3273	−	12.1284i	−1.20915	−	0.392876i	−0.843119	+	0.537727i	$0.819283\pi$
$954$	−5.62118	+	2.62634i	−0.181992	+	0.0850308i
$955$	−13.9749	+	10.1534i	−0.452218	+	0.328556i
$956$	30.9716	−	7.77148i	1.00169	−	0.251348i
$957$	8.98407	+	11.1271i	0.290414	+	0.359688i
$958$	22.3372	−	2.75968i	0.721684	−	0.0891612i
$959$	−3.95392	+	2.87269i	−0.127679	+	0.0927641i
$960$	2.76361	−	4.83687i	0.0891952	−	0.156109i
$961$	−5.44555	+	16.7597i	−0.175663	+	0.540635i
$962$	8.85911	−	16.0106i	0.285629	−	0.516202i
$963$	4.87127	−	6.70473i	0.156974	−	0.216057i
$964$	18.8107	+	1.28701i	0.605853	+	0.0414520i
$965$	−0.00505327	−	0.0155524i	−0.000162670	−	0.000500648i
$966$	13.7826	+	14.7578i	0.443449	+	0.474826i
$967$	−35.8221			−1.15196			−0.575980	−	0.817464i	$-0.695379\pi$
$967$	−35.8221			−1.15196			−0.575980	+	0.817464i	$0.695379\pi$
$968$	27.7305	−	14.1075i	0.891291	−	0.453431i
$969$	−22.6146			−0.726484
$970$	2.89600	+	3.10091i	0.0929849	+	0.0995643i
$971$	−9.05079	−	27.8555i	−0.290454	−	0.893924i	−0.984711	−	0.174197i	$-0.944267\pi$
$971$	−9.05079	−	27.8555i	−0.290454	−	0.893924i	0.694257	−	0.719727i	$-0.255733\pi$
$972$	−0.136519	+	1.99534i	−0.00437885	+	0.0640004i
$973$	1.53300	−	2.11000i	0.0491458	−	0.0676434i
$974$	25.9793	−	46.9510i	0.832431	−	1.50441i
$975$	−8.48539	+	26.1153i	−0.271750	+	0.836360i
$976$	0.854820	+	0.820547i	0.0273621	+	0.0262651i
$977$	−19.3774	+	14.0785i	−0.619939	+	0.450412i	−0.852900	−	0.522074i	$-0.825159\pi$
$977$	−19.3774	+	14.0785i	−0.619939	+	0.450412i	0.232961	+	0.972486i	$0.425159\pi$
$978$	1.06267	−	0.131289i	0.0339806	−	0.00419817i
$979$	−13.8188	−	17.1151i	−0.441651	−	0.547001i
$980$	−1.44817	−	5.77139i	−0.0462601	−	0.184360i
$981$	14.3828	−	10.4497i	0.459208	−	0.333634i
$982$	0.707164	−	0.330402i	0.0225665	−	0.0105436i
$983$	15.5566	+	5.05465i	0.496179	+	0.161218i	0.546408	−	0.837519i	$-0.315995\pi$
$983$	15.5566	+	5.05465i	0.496179	+	0.161218i	−0.0502286	+	0.998738i	$0.515995\pi$
$984$	−0.562428	+	2.11807i	−0.0179295	+	0.0675215i
$985$	−0.0750876	+	0.103349i	−0.00239249	+	0.00329298i
$986$	22.7317	+	4.40090i	0.723925	+	0.140153i
$987$	−8.74929	+	2.84282i	−0.278493	+	0.0904879i
$988$	55.5660	+	46.4835i	1.76779	+	1.47884i
$989$	87.9459			2.79652
$990$	−0.456784	+	3.23402i	−0.0145175	+	0.102784i
$991$			54.9239i			1.74471i	0.488870	+	0.872357i	$0.337409\pi$
$991$			54.9239i			1.74471i	−0.488870	+	0.872357i	$0.662591\pi$
$992$	−37.3439	−	12.7020i	−1.18567	−	0.403290i
$993$	−2.79706	−	8.60845i	−0.0887619	−	0.273181i
$994$	4.44894	+	0.861322i	0.141112	+	0.0273195i
$995$	−8.33932	−	6.05887i	−0.264374	−	0.192079i
$996$	2.42403	−	6.02571i	0.0768084	−	0.190932i
$997$	2.82716	−	8.70110i	0.0895370	−	0.275567i	−0.896254	−	0.443540i	$-0.853722\pi$
$997$	2.82716	−	8.70110i	0.0895370	−	0.275567i	0.985791	+	0.167974i	$0.0537223\pi$
$998$	−1.43998	−	3.08200i	−0.0455817	−	0.0975590i
$999$	−1.25052	−	1.72119i	−0.0395646	−	0.0544561i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	264.2.z.b.19.9	yes	48
3.2	odd	2		792.2.bp.d.19.4		48
4.3	odd	2		1056.2.bp.a.943.7		48
8.3	odd	2	inner	264.2.z.b.19.3	✓	48
8.5	even	2		1056.2.bp.a.943.6		48
11.7	odd	10	inner	264.2.z.b.139.3	yes	48
24.11	even	2		792.2.bp.d.19.10		48
33.29	even	10		792.2.bp.d.667.10		48
44.7	even	10		1056.2.bp.a.271.6		48
88.29	odd	10		1056.2.bp.a.271.7		48
88.51	even	10	inner	264.2.z.b.139.9	yes	48
264.227	odd	10		792.2.bp.d.667.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
264.2.z.b.19.3	✓	48	8.3	odd	2	inner
264.2.z.b.19.9	yes	48	1.1	even	1	trivial
264.2.z.b.139.3	yes	48	11.7	odd	10	inner
264.2.z.b.139.9	yes	48	88.51	even	10	inner
792.2.bp.d.19.4		48	3.2	odd	2
792.2.bp.d.19.10		48	24.11	even	2
792.2.bp.d.667.4		48	264.227	odd	10
792.2.bp.d.667.10		48	33.29	even	10
1056.2.bp.a.271.6		48	44.7	even	10
1056.2.bp.a.271.7		48	88.29	odd	10
1056.2.bp.a.943.6		48	8.5	even	2
1056.2.bp.a.943.7		48	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 264 = 2^{3} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	264.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.03357 - 0.965267i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.136519 - 1.99534i) q^{4} +(0.409298 - 0.563350i) q^{5} +(-1.23741 - 0.684696i) q^{6} +(0.510340 - 1.57067i) q^{7} +(-1.78493 - 2.19409i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.120747 - 0.977341i) q^{10} +(2.08351 + 2.58050i) q^{11} +(-1.93986 + 0.486755i) q^{12} +(-4.92015 + 3.57470i) q^{13} +(-0.988641 - 2.11600i) q^{14} +(-0.662258 - 0.215181i) q^{15} +(-3.96273 - 0.544803i) q^{16} +(2.23176 - 3.07176i) q^{17} +(-0.268803 + 1.38843i) q^{18} +(5.66454 - 1.84052i) q^{19} +(-1.06820 - 0.893594i) q^{20} -1.65150 q^{21} +(4.64432 + 0.655979i) q^{22} -8.64584i q^{23} +(-1.53513 + 2.37558i) q^{24} +(1.39525 + 4.29413i) q^{25} +(-1.63476 + 8.44395i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-3.06433 - 1.23273i) q^{28} +(-1.33248 + 4.10095i) q^{29} +(-0.892194 + 0.416852i) q^{30} +(4.09860 + 5.64124i) q^{31} +(-4.62162 + 3.26200i) q^{32} +(1.81036 - 2.77895i) q^{33} +(-0.658392 - 5.32912i) q^{34} +(-0.675953 - 0.930370i) q^{35} +(1.06238 + 1.69450i) q^{36} +(-2.02338 - 0.657436i) q^{37} +(4.07809 - 7.37010i) q^{38} +(4.92015 + 3.57470i) q^{39} +(-1.96661 + 0.107505i) q^{40} +(0.736879 - 0.239427i) q^{41} +(-1.70693 + 1.59413i) q^{42} +10.1720i q^{43} +(5.43341 - 3.80501i) q^{44} +0.696339i q^{45} +(-8.34554 - 8.93605i) q^{46} +(5.29780 - 1.72136i) q^{47} +(0.706411 + 3.93713i) q^{48} +(3.45658 + 2.51135i) q^{49} +(5.58706 + 3.09148i) q^{50} +(-3.61107 - 1.17331i) q^{51} +(6.46103 + 10.3054i) q^{52} +(2.57874 + 3.54933i) q^{53} +(1.40354 - 0.173402i) q^{54} +(2.30650 - 0.117551i) q^{55} +(-4.35710 + 1.68380i) q^{56} +(-3.50088 - 4.81855i) q^{57} +(2.58130 + 5.52480i) q^{58} +(3.78102 - 11.6368i) q^{59} +(-0.519768 + 1.29205i) q^{60} +(-0.239653 - 0.174118i) q^{61} +(9.68148 + 1.87435i) q^{62} +(0.510340 + 1.57067i) q^{63} +(-1.62805 + 7.83259i) q^{64} +4.23488i q^{65} +(-0.811300 - 4.61972i) q^{66} -10.7130 q^{67} +(-5.82451 - 4.87247i) q^{68} +(-8.22268 + 2.67171i) q^{69} +(-1.59670 - 0.309124i) q^{70} +(-1.14044 + 1.56968i) q^{71} +(2.73369 + 0.725900i) q^{72} +(-6.90989 - 2.24516i) q^{73} +(-2.72590 + 1.27360i) q^{74} +(3.65280 - 2.65392i) q^{75} +(-2.89914 - 11.5539i) q^{76} +(5.11640 - 1.95556i) q^{77} +(8.53584 - 1.05457i) q^{78} +(2.76926 - 2.01198i) q^{79} +(-1.92885 + 2.00941i) q^{80} +(0.309017 - 0.951057i) q^{81} +(0.530503 - 0.958748i) q^{82} +(-1.90883 + 2.62729i) q^{83} +(-0.225461 + 3.29529i) q^{84} +(-0.817020 - 2.51453i) q^{85} +(9.81874 + 10.5135i) q^{86} +4.31199 q^{87} +(1.94294 - 9.17742i) q^{88} -6.63247 q^{89} +(0.672153 + 0.719713i) q^{90} +(3.10371 + 9.55222i) q^{91} +(-17.2513 - 1.18032i) q^{92} +(4.09860 - 5.64124i) q^{93} +(3.81406 - 6.89293i) q^{94} +(1.28163 - 3.94444i) q^{95} +(4.53050 + 3.38741i) q^{96} +(-3.48568 + 2.53250i) q^{97} +(5.99672 - 0.740872i) q^{98} +(-3.20237 - 0.863015i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{3} + 4 q^{4} - 12 q^{9} + 4 q^{11} + 6 q^{12} - 16 q^{14} + 20 q^{16} - 5 q^{18} + 25 q^{20} + 3 q^{22} + 20 q^{24} - 4 q^{25} + 4 q^{26} + 12 q^{27} - 25 q^{28} - 10 q^{30} - 4 q^{33} + 4 q^{36}+ \cdots - 16 q^{99}+O(q^{100}) \) 48 * q + 12 * q^3 + 4 * q^4 - 12 * q^9 + 4 * q^11 + 6 * q^12 - 16 * q^14 + 20 * q^16 - 5 * q^18 + 25 * q^20 + 3 * q^22 + 20 * q^24 - 4 * q^25 + 4 * q^26 + 12 * q^27 - 25 * q^28 - 10 * q^30 - 4 * q^33 + 4 * q^36 + 26 * q^38 - 65 * q^40 - 60 * q^41 - 4 * q^42 - 43 * q^44 - 5 * q^46 + 5 * q^48 - 12 * q^49 - 80 * q^50 - 15 * q^52 - 14 * q^56 + 73 * q^58 - 8 * q^59 - 25 * q^60 - 45 * q^62 - 38 * q^64 - 13 * q^66 + 8 * q^67 - 55 * q^68 - 40 * q^70 + 20 * q^72 + 60 * q^74 - 36 * q^75 + 46 * q^78 - 12 * q^81 - 35 * q^82 - 100 * q^83 + 45 * q^84 + 81 * q^86 - 18 * q^88 + 96 * q^89 + 10 * q^90 - 20 * q^91 + 59 * q^92 + 35 * q^94 - 40 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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